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zzy0H3ZbWiHsS
|
Audio Artist Identification by Deep Neural Network
|
Since officially began in 2005, the annual Music Information Retrieval Evaluation eXchange (MIREX) has made great contributions to the Music Information Retrieval (MIR) research. By defining some important tasks and providing a meaningful comparison system, the International Music Information Retrieval Systems Evaluation Laboratory (IMIRSEL), organizer of the MIREX, drives researchers in the MIR field to develop more advanced system to fulfill the tasks. One of the important tasks is the Audio Artist Identification task, or the AAI task. We implemented a Deep Belief Network (DBN) to identify the artist by audio signal. As a matter of copyright, IMIRSEL didn't publish there data set and we had to construct our own. In our data set we got an accuracy of 69.87% without carefully choosing parameters while the best result reported on MIREX is 69.70%. We think our method is promising and we want to discuss with others.
|
胡振, Kun Fu, Changshui Zhang
|
Unknown
| 2,013
|
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|
[Review]:
Thank you. We will revise our paper as soon as possible.
Zhen
|
胡振
| null | null |
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iclr2013
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zzy0H3ZbWiHsS
|
Audio Artist Identification by Deep Neural Network
|
Since officially began in 2005, the annual Music Information Retrieval Evaluation eXchange (MIREX) has made great contributions to the Music Information Retrieval (MIR) research. By defining some important tasks and providing a meaningful comparison system, the International Music Information Retrieval Systems Evaluation Laboratory (IMIRSEL), organizer of the MIREX, drives researchers in the MIR field to develop more advanced system to fulfill the tasks. One of the important tasks is the Audio Artist Identification task, or the AAI task. We implemented a Deep Belief Network (DBN) to identify the artist by audio signal. As a matter of copyright, IMIRSEL didn't publish there data set and we had to construct our own. In our data set we got an accuracy of 69.87% without carefully choosing parameters while the best result reported on MIREX is 69.70%. We think our method is promising and we want to discuss with others.
|
胡振, Kun Fu, Changshui Zhang
|
Unknown
| 2,013
|
{"id": "zzy0H3ZbWiHsS", "original": null, "cdate": null, "pdate": null, "odate": null, "mdate": null, "tcdate": 1358325000000, "tmdate": 1358325000000, "ddate": null, "number": 1, "content": {"decision": "reject", "title": "Audio Artist Identification by Deep Neural Network", "abstract": "Since officially began in 2005, the annual Music Information Retrieval Evaluation eXchange (MIREX) has made great contributions to the Music Information Retrieval (MIR) research. By defining some important tasks and providing a meaningful comparison system, the International Music Information Retrieval Systems Evaluation Laboratory (IMIRSEL), organizer of the MIREX, drives researchers in the MIR field to develop more advanced system to fulfill the tasks. One of the important tasks is the Audio Artist Identification task, or the AAI task. We implemented a Deep Belief Network (DBN) to identify the artist by audio signal. As a matter of copyright, IMIRSEL didn't publish there data set and we had to construct our own. In our data set we got an accuracy of 69.87% without carefully choosing parameters while the best result reported on MIREX is 69.70%. We think our method is promising and we want to discuss with others.", "pdf": "https://arxiv.org/abs/1301.3195", "paperhash": "|audio_artist_identification_by_deep_neural_network", "keywords": [], "conflicts": [], "authors": ["\u80e1\u632f", "Kun Fu", "Changshui Zhang"], "authorids": ["eblis.hu@gmail.com", "Tsinghua Univ.", "Tsinghua Univ."]}, "forum": "zzy0H3ZbWiHsS", "referent": null, "invitation": "ICLR.cc/2013/conference/-/submission", "replyto": null, "readers": ["everyone"], "nonreaders": [], "signatures": ["eblis.hu@gmail.com"], "writers": []}
|
[Review]:
This paper present an application of an hybrid deep learning model to the task of audio artist identification.
Novelty:
+ The novelty of the paper comes from using an hybrid unsupervised learning approach by stacking Denoising Auto-Encoders (DA) and Restricted Boltzman Machines (RBM).
= Another minor novelty is the application of deep learning to artist identification. However, deep learning has already been applied to similar tasks before such as genre recognition and automatic tag annotation.
- Unfortunately, I found that the major contributions of the paper are not exposed clearly enough in the introduction.
Quality of presentation:
- The quality of the presentation leaves to be desired. A more careful proofreading would have been required. There are several sentences with gramatical errors. Several verbs or adjectives are wrong. The writing style is also sometimes inadequate for a scientific paper (ex. 'we will review some fantastic work', 'we can build many outstanding networks'). The quality of the english is, in general, inadequate.
- The abstract does not present in a relevant and concise manner the essential points of the paper.
- Also, there is a bit of confusion in between the introduction and related work sections, as most of the introduction is also about related work.
Reference to previous work:
+ Previous related work coverage is good. Previous work in deep learning and its applications in MIR, as well as work in audio artist identification are well covered.
- In the beginning of section 5: 'It's known that Bach, Beethoven and Brahms, known as the three Bs, shared some style when they wrote their composition.' I find this claim, without any reference, hard to understand. Bach, Beethoven and Brahms are from 3 different musical eras. How are these 3 composers more related than the others?
Quality of the research.
- Although the idea of using a hybrid deep learning system might be new, no justification as to why such a system should work better is presented in the paper.
- In the experiments, the authors compare the hybrid model to pure models. However, the pure models all have less layers than the hybrid model. Why didn't the authors compare same-depth models? I feel it would have made a much stronger point.
- Although the authors describe in details the theory behind SDAs and DBNs, there is little to no detail about the hyper-parameters used in the actual model (number of hidden units, number of unsupervised epochs, regularization, etc.). How was the data corrupted for the DA? White Noise, or random flipped bits? How many steps in the CD? These details would be important to reproduce the results.
- In the beginning of section 3 and 6, the authors mention that they think their model will project the data into a semantic space which is very sparse. How is your model learning a sparse representation? Have you used sparseness constraints in your training? If so, there is no mention of it in the paper.
|
anonymous reviewer 8eb9
| null | null |
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| 1.314286
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iclr2013
|
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zzy0H3ZbWiHsS
|
Audio Artist Identification by Deep Neural Network
|
Since officially began in 2005, the annual Music Information Retrieval Evaluation eXchange (MIREX) has made great contributions to the Music Information Retrieval (MIR) research. By defining some important tasks and providing a meaningful comparison system, the International Music Information Retrieval Systems Evaluation Laboratory (IMIRSEL), organizer of the MIREX, drives researchers in the MIR field to develop more advanced system to fulfill the tasks. One of the important tasks is the Audio Artist Identification task, or the AAI task. We implemented a Deep Belief Network (DBN) to identify the artist by audio signal. As a matter of copyright, IMIRSEL didn't publish there data set and we had to construct our own. In our data set we got an accuracy of 69.87% without carefully choosing parameters while the best result reported on MIREX is 69.70%. We think our method is promising and we want to discuss with others.
|
胡振, Kun Fu, Changshui Zhang
|
Unknown
| 2,013
|
{"id": "zzy0H3ZbWiHsS", "original": null, "cdate": null, "pdate": null, "odate": null, "mdate": null, "tcdate": 1358325000000, "tmdate": 1358325000000, "ddate": null, "number": 1, "content": {"decision": "reject", "title": "Audio Artist Identification by Deep Neural Network", "abstract": "Since officially began in 2005, the annual Music Information Retrieval Evaluation eXchange (MIREX) has made great contributions to the Music Information Retrieval (MIR) research. By defining some important tasks and providing a meaningful comparison system, the International Music Information Retrieval Systems Evaluation Laboratory (IMIRSEL), organizer of the MIREX, drives researchers in the MIR field to develop more advanced system to fulfill the tasks. One of the important tasks is the Audio Artist Identification task, or the AAI task. We implemented a Deep Belief Network (DBN) to identify the artist by audio signal. As a matter of copyright, IMIRSEL didn't publish there data set and we had to construct our own. In our data set we got an accuracy of 69.87% without carefully choosing parameters while the best result reported on MIREX is 69.70%. We think our method is promising and we want to discuss with others.", "pdf": "https://arxiv.org/abs/1301.3195", "paperhash": "|audio_artist_identification_by_deep_neural_network", "keywords": [], "conflicts": [], "authors": ["\u80e1\u632f", "Kun Fu", "Changshui Zhang"], "authorids": ["eblis.hu@gmail.com", "Tsinghua Univ.", "Tsinghua Univ."]}, "forum": "zzy0H3ZbWiHsS", "referent": null, "invitation": "ICLR.cc/2013/conference/-/submission", "replyto": null, "readers": ["everyone"], "nonreaders": [], "signatures": ["eblis.hu@gmail.com"], "writers": []}
|
[Review]:
This paper describes work to collect a new dataset with music from 11 classical composers for the task of audio composer identification (although the title, abstract, and introduction use the phrase 'audio artist identification' which is a different task). It describes experiments training a few different deep neural networks to perform this classification task.
The paper is not very novel. It describes existing deep architectures applied to a new version of an existing dataset for an existing task.
The quality of the paper is not very high. The comparisons of the models were not systematic and because it is a new dataset, they cannot be compared directly to results on other datasets of existing models. There are very few specifics given about the models used (layer sizes, cost functions, input feature types, specific input features).
The use of mel frequency spectrum seems dubious for this task. What distinguishes classical works from different composers is generally harmonic and melodic content, which mel frequency spectrum ignores almost entirely.
Few details are given about the make-up of the new dataset. Are these orchestral pieces, chamber pieces, concertos, piano pieces, etc? How many clips came from each piece? How many clips came from each movement? The use of clips from different movements of the same piece in the training and test sets might account for the increase in accuracy scores relative to previous MIREX results. Movements from the same piece generally share many characteristics like recording conditions, production, instrumentation, and timbre, which are the main characteristics captured by mel frequency spectrum. They also generally share harmonic and melodic content.
And finally, the 'Three B's' that the authors refer to, Bach, Beethoven, and Brahms, are very different composers from different musical eras. Their works should not be easily confused with each other, and so the fact that the proposed algorithm does confuse them is concerning. Potentially it indicates the weakness of the mel spectrum for performing this task.
Pros:
- Literary presentation of the paper is high (although there are a number of strange word substitutions)
- Decent summary of existing work
- New dataset might be useful, if it is made public, although it is pretty small
Cons:
- Little novelty
- Un-systematic comparisons of systems
- Features don't make much sense
- Few details on actual systems compared and on the dataset
- Few generalizable conclusions
|
anonymous reviewer b7e1
| null | null |
{"id": "k3fr32tl6qARo", "original": null, "cdate": null, "pdate": null, "odate": null, "mdate": null, "tcdate": 1362226800000, "tmdate": 1362226800000, "ddate": null, "number": 4, "content": {"title": "review of Audio Artist Identification by Deep Neural Network", "review": "This paper describes work to collect a new dataset with music from 11 classical composers for the task of audio composer identification (although the title, abstract, and introduction use the phrase 'audio artist identification' which is a different task). It describes experiments training a few different deep neural networks to perform this classification task.\r\n\r\nThe paper is not very novel. It describes existing deep architectures applied to a new version of an existing dataset for an existing task.\r\n\r\nThe quality of the paper is not very high. The comparisons of the models were not systematic and because it is a new dataset, they cannot be compared directly to results on other datasets of existing models. There are very few specifics given about the models used (layer sizes, cost functions, input feature types, specific input features).\r\n\r\nThe use of mel frequency spectrum seems dubious for this task. What distinguishes classical works from different composers is generally harmonic and melodic content, which mel frequency spectrum ignores almost entirely.\r\n\r\nFew details are given about the make-up of the new dataset. Are these orchestral pieces, chamber pieces, concertos, piano pieces, etc? How many clips came from each piece? How many clips came from each movement? The use of clips from different movements of the same piece in the training and test sets might account for the increase in accuracy scores relative to previous MIREX results. Movements from the same piece generally share many characteristics like recording conditions, production, instrumentation, and timbre, which are the main characteristics captured by mel frequency spectrum. They also generally share harmonic and melodic content.\r\n\r\nAnd finally, the 'Three B's' that the authors refer to, Bach, Beethoven, and Brahms, are very different composers from different musical eras. Their works should not be easily confused with each other, and so the fact that the proposed algorithm does confuse them is concerning. Potentially it indicates the weakness of the mel spectrum for performing this task.\r\n\r\nPros:\r\n- Literary presentation of the paper is high (although there are a number of strange word substitutions)\r\n- Decent summary of existing work\r\n- New dataset might be useful, if it is made public, although it is pretty small\r\n\r\nCons:\r\n- Little novelty\r\n- Un-systematic comparisons of systems\r\n- Features don't make much sense\r\n- Few details on actual systems compared and on the dataset\r\n- Few generalizable conclusions"}, "forum": "zzy0H3ZbWiHsS", "referent": null, "invitation": "ICLR.cc/2013/-/submission/review", "replyto": "zzy0H3ZbWiHsS", "readers": ["everyone"], "nonreaders": [], "signatures": ["anonymous reviewer b7e1"], "writers": ["anonymous"]}
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iclr2013
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zzy0H3ZbWiHsS
|
Audio Artist Identification by Deep Neural Network
|
Since officially began in 2005, the annual Music Information Retrieval Evaluation eXchange (MIREX) has made great contributions to the Music Information Retrieval (MIR) research. By defining some important tasks and providing a meaningful comparison system, the International Music Information Retrieval Systems Evaluation Laboratory (IMIRSEL), organizer of the MIREX, drives researchers in the MIR field to develop more advanced system to fulfill the tasks. One of the important tasks is the Audio Artist Identification task, or the AAI task. We implemented a Deep Belief Network (DBN) to identify the artist by audio signal. As a matter of copyright, IMIRSEL didn't publish there data set and we had to construct our own. In our data set we got an accuracy of 69.87% without carefully choosing parameters while the best result reported on MIREX is 69.70%. We think our method is promising and we want to discuss with others.
|
胡振, Kun Fu, Changshui Zhang
|
Unknown
| 2,013
|
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|
[Review]:
A brief summary of the paper’s contributions. In the context of prior work:
This paper builds a hybrid model based on Deep Belief Network (DBN) and Stacked Denoising Autoencoder (SDA) and applies it to Audio Artist Identification (AAI) task. Specifically, the proposed model is constructed with a two-layer SDA in the lower layers, a two-layer DBN in the middle, and a logistic regression classification layer on the top. The proposed model seems to achieve good classification performance.
An assessment of novelty and quality:
The paper proposes a hybrid deep network by stacking denoising autoencoders and RBMs.
Although this may be a new way of building a deep network, it seems to be a minor modification of the standard methods. Therefore, the novelty seems to be limited.
More importantly, motivation or justification about hybrid architecture is not clearly presented. Without a clear motivation or justification, this method doesn’t seem to be technically interesting. To make a fair comparison to other baseline methods, the SDA2-DBN2 should be compared to DBN4 or SDA4, but there are no such comparisons.
Although the classification performance by the proposed method is good, the results are not directly comparable to other work in the literature. It will be helpful to apply some widely used methods in authors’ data set as additional control experiments;
The paper isn’t well polished. There are many awkward sentences and grammatical errors.
Other comments:
Figure 2 is anecdotal and is not convincing enough.
Authors use some non-standard terminology. For example, what does “MAP paradigm” mean?
In Table 3, rows corresponding to “#DA layers”, “#RBM layers”, “#logistic layers” are unnecessary.
A list of pros and cons (reasons to accept/reject)
pros:
+ Literature review seems fine.
+ good (but incomplete) empirical classification results
cons:
- lack of clear motivation or justification of the hybrid method; lack of proper control experiments
- the results are not comparable to other published work
- unpolished writing (lots of awkward sentences and grammatical errors).
|
anonymous reviewer 589d
| null | null |
{"id": "Zg8fgYb5dAUiY", "original": null, "cdate": null, "pdate": null, "odate": null, "mdate": null, "tcdate": 1362479820000, "tmdate": 1362479820000, "ddate": null, "number": 1, "content": {"title": "review of Audio Artist Identification by Deep Neural Network", "review": "A brief summary of the paper\u2019s contributions. In the context of prior work:\r\nThis paper builds a hybrid model based on Deep Belief Network (DBN) and Stacked Denoising Autoencoder (SDA) and applies it to Audio Artist Identification (AAI) task. Specifically, the proposed model is constructed with a two-layer SDA in the lower layers, a two-layer DBN in the middle, and a logistic regression classification layer on the top. The proposed model seems to achieve good classification performance.\r\n\r\n\r\nAn assessment of novelty and quality:\r\nThe paper proposes a hybrid deep network by stacking denoising autoencoders and RBMs.\r\nAlthough this may be a new way of building a deep network, it seems to be a minor modification of the standard methods. Therefore, the novelty seems to be limited.\r\n\r\nMore importantly, motivation or justification about hybrid architecture is not clearly presented. Without a clear motivation or justification, this method doesn\u2019t seem to be technically interesting. To make a fair comparison to other baseline methods, the SDA2-DBN2 should be compared to DBN4 or SDA4, but there are no such comparisons.\r\n\r\nAlthough the classification performance by the proposed method is good, the results are not directly comparable to other work in the literature. It will be helpful to apply some widely used methods in authors\u2019 data set as additional control experiments;\r\n\r\nThe paper isn\u2019t well polished. There are many awkward sentences and grammatical errors.\r\n\r\n\r\nOther comments:\r\nFigure 2 is anecdotal and is not convincing enough.\r\n\r\nAuthors use some non-standard terminology. For example, what does \u201cMAP paradigm\u201d mean?\r\n\r\nIn Table 3, rows corresponding to \u201c#DA layers\u201d, \u201c#RBM layers\u201d, \u201c#logistic layers\u201d are unnecessary.\r\n\r\n\r\n\r\nA list of pros and cons (reasons to accept/reject)\r\n\r\npros:\r\n+ Literature review seems fine.\r\n+ good (but incomplete) empirical classification results\r\n\r\ncons:\r\n- lack of clear motivation or justification of the hybrid method; lack of proper control experiments\r\n- the results are not comparable to other published work\r\n- unpolished writing (lots of awkward sentences and grammatical errors)."}, "forum": "zzy0H3ZbWiHsS", "referent": null, "invitation": "ICLR.cc/2013/-/submission/review", "replyto": "zzy0H3ZbWiHsS", "readers": ["everyone"], "nonreaders": [], "signatures": ["anonymous reviewer 589d"], "writers": ["anonymous"]}
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zzKhQhsTYlzAZ
|
Regularized Discriminant Embedding for Visual Descriptor Learning
|
Images can vary according to changes in viewpoint, resolution, noise, and illumination. In this paper, we aim to learn representations for an image, which are robust to wide changes in such environmental conditions, using training pairs of matching and non-matching local image patches that are collected under various environmental conditions. We present a regularized discriminant analysis that emphasizes two challenging categories among the given training pairs: (1) matching, but far apart pairs and (2) non-matching, but close pairs in the original feature space (e.g., SIFT feature space). Compared to existing work on metric learning and discriminant analysis, our method can better distinguish relevant images from irrelevant, but look-alike images.
|
Regularized Discriminant Embedding for Visual
Descriptor Learning
Kye-Hyeon Kim,a Rui Cai,b Lei Zhang,b Seungjin Choia∗
a Department of Computer Science, POSTECH, Pohang 790-784, Korea
b Microsoft Research Asia, Beijing 100080, China
fenrir@postech.ac.kr, {ruicai, leizhang}@microsoft.com,
seungjin@postech.ac.kr
Abstract
Images can vary according to changes in viewpoint, resolution, noise, and illu-
mination. In this paper, we aim to learn representations for an image, which are
robust to wide changes in such environmental conditions, using training pairs of
matching and non-matching local image patches that are collected under various
environmental conditions. We present a regularized discriminant analysis that em-
phasizes two challenging categories among the given training pairs: (1) matching,
but far apart pairs and (2) non-matching, but close pairs in the original feature
space (e.g., SIFT feature space). Compared to existing work on metric learning
and discriminant analysis, our method can better distinguish relevant images from
irrelevant, but look-alike images.
1 Introduction
In many computer vision problems, images are compared using their local descriptors. A local
descriptor is a feature vector, representing characteristics of an interesting local partin an image.
Scale-invariant feature transform (SIFT) [2] is popularly used for extracting interesting parts and
their local descriptors from an image. Then comparing two images is done by aggregating pairs
between each local descriptor in one image and its closest local descriptor in another image, whose
pairwise distances are below some threshold. The assumption behind this procedure is that local
descriptors corresponding to the same local part (“matching descriptors”) are usually close enough
in the feature space, whereas local descriptors belonging to different local parts (“non-matching
descriptors”) are far apart.
However, this assumption does not hold when there are significant changes in environmental condi-
tions (e.g., viewpoint, illumination, noise, and resolution) between two images. For the same local
part, varying environment conditions can yield varying local image patches, leading to matching
descriptors far apartin the feature space. On the other hand, for different local parts, their image
patches can look similar to each other in some environmental conditions, leading to non-matching
descriptors close together. Fig. 1 shows some examples: in each triplet, the first two image patches
belong to the same local part but captured under different environment conditions, while the third
patch belongs to a different part but looks similar to the second one, resulting that the SIFT descrip-
tors between non-matching local parts are closer than those between matching parts. Consequently,
comparing two images using their local descriptors cannot be done correctly when their are signifi-
cant differences in environmental conditions between the images. Fig. 2(a) shows the cases.
In this paper, we address this problem by learning more robust representations for local image
patches where matching parts are more similar together than non-matching parts even under widely
varying environmental conditions.
∗The full version of this manuscript is currently under review in an international journal.
1
arXiv:1301.3644v1 [cs.CV] 16 Jan 2013
SIFT: 304
LDE: 336
Ours: 360
SIFT: 213
LDE: 268
Ours: 295
SIFT: 268
LDE: 283
Ours: 301
231
275
425
SIFT: 336
LDE: 371
Ours: 362
>
>
<
246
314
372
>
≈
<
199
264
388
SIFT: 267
LDE: 240
Ours: 257
>
<
<
257
319
405
>
<
<
232
291
335
SIFT: 290
LDE: 305
Ours: 349
>
>
<
221
278
365
>
>
<
Figure 1: Some examples where a local part (center in each triplet) is closer to a non-matching part
(right) than a matching part (left) in terms of the Euclidean distances between their SIFT descriptors.
Using linear discriminant embedding (LDE) [1], non-matching pairs are still closer than matching
pairs in the first three examples. Compared to existing work on metric learning and discriminant
analysis, our learning method focuses more on “far but matching” and “close but non-matching”
training pairs, so that can distinguish look-alike irrelevant parts successfully.
(a) 15 closest SIFT pairs
(b) 15 closest RDE pairs
Figure 2: (a) When two images of the same scene are captured under considerably different con-
ditions, many irrelevant pairs of local parts are chosen as closest pairs in the local feature space,
which may lead to undesirable results of comparison. (b) In our RDE space, matching pairs are
successfully chosen as closest pairs.
2 Proposed Method
In descriptor learning [1, 3], a projection is obtained from training pairs of matching and non-
matching descriptors in order to map given local descriptors (e.g., SIFT) to a new feature space
where matching descriptors are closer to each other and non-matching descriptors are farther from
each other. Traditional techniques for supervised dimensionality reduction, including linear discrim-
inant analysis (LDA) and local Fisher discriminant analysis (LFDA) [4], can be applied to descriptor
learning after a slight modification. For example, linear discriminant embedding (LDE) [1] is come
from LDA with a simple modification for handling pairwise training data.
We propose a regularized learning framework in order to further emphasize (1) matching, but far
apart pairs and (2) non-matching, but look-alike pairs, under wide environmental conditions. First,
we divide given training pairs of local descriptors into four subsets, Relevant-Near (Rel-Near),
Relevant-Far (Rel-Far), Irrelevant-Near (Irr-Near), and Irrelevant-Far (Irr-Far). For example, the
“Irr-Near” subset consists of irrelevant (i.e., non-matching), but near pairs. We define an irrelevant
pair (xi,xj) as “near” ifxi is one of the knearest descriptors1 among all non-matching descriptors
of xj or vice versa. Similarly, a relevant pair (xi,xj) is called “near” if xi is one of knearest de-
scriptors among all matching descriptors of xj. All the other pairs belong to “Irr-Far” or “Rel-Far”.
Then we seek a linear projection T that maximizes the following regularized ratio:
J(T) =
βIN
∑
(i,j)∈PIN
dij(T) +βIF
∑
(i,j)∈PIF
dij(T)
βRN
∑
(i,j)∈PRN
dij(T) +βRF
∑
(i,j)∈PRF
dij(T) , (1)
1In our experiments, setting 1 ≤ k ≤ 10 achieved a reasonable performance improvement.
2
−1 −0.5 0 0.5 1
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
LDE
LFDA
RDE
(a)
−1 −0.5 0 0.5 1
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
LDE
LFDA
RDE (b)
Figure 3: Toy examples of projections learned by LDE, LFDA, and our RDE.
0 100 200 300 400 500 600 7000
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Distance
The number of pairs
Err (Rel vs Irr) = 15.58%
Err (RFar vs INear) = 29.92%
RelNear
IrrFar
IrrNear
RelFar
(a) SIFT feature space
0 100 200 300 400 500 600 7000
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Distance
The number of pairs
Err (Rel vs Irr) = 13.99%
Err (RFar vs INear) = 27.00%
RelNear
IrrFar
IrrNear
RelFar (b) LDE feature space
0 100 200 300 400 500 600 7000
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Distance
The number of pairs
Err (Rel vs Irr) = 8.34%
Err (RFar vs INear) = 16.30%
RelNear
IrrFar
IrrNear
RelFar (c) Our RDE feature space
Figure 4: Distribution of Euclidean distance in a given feature space for each subset of pairs. Err
(Rel vs Irr)measures the proportion of overlapping region between {Rel-Near, Rel-Far}and {Irr-
Near, Irr-Far}, while Err (RFar vs INear)measures the overlap between Rel-Far and Irr-Near. In
our RDE space, non-matching pairs are well distinguished from matching pairs.
where dij(T) denotes the squared distance ||T(xi −xj)||2 between two local descriptors xi and xj
in the projected space, and PRN ,PRF ,PIN ,PIF denote the subsets of Rel-Near, Rel-Far, Irr-Near,
and Irr-Far, respectively. Four regularization constantsβRN ,βRF ,βIN ,βIF control the importance
of each subset.
• In LDE, all pairs are equally important, i.e., βRN = βRF = βIN = βIF = 1.
• In LFDA , “near” pairs are more important, i.e.,βRN ≫βRF and βIN ≫βIF .
• In our method, we propose to emphasize Rel-Far (matching but far apart) and Irr-Near
(non-matching but close) pairs, i.e., βRN ≪βRF and βIN ≫βIF .
Fig. 3 shows when and why our method can better distinguish Irr-Near pairs from Rel-Far pairs.
In Fig. 3(a), the global intra-class distribution forms a diagonal, while each local cluster has no
meaningful direction of scattering. Since LFDA focuses on “near” pairs, it cannot capture the true
intra-class scatter well, leading to the undesirable projection. In Fig. 3(b), LDE obtains a projection
that maximizes the inter-class variance, but the shape of the class boundary cannot be considered
well, leading to an overlap between two classes. In this case, focusing more on Irr-Near pairs (i.e.,
the pairs of opposite clusters near the class boundary) can preserve the separability of classes.
Fig. 4 shows the distance distribution of local descriptors, where 20,000 pairs of each subset are
randomly chosen from 500,000 local patches of Flickr images. As shown in Fig. 4(a), Rel-Near
and Irr-Far pairs are already well separated in the SIFT space, but Rel-Far and Irr-Near pairs are
not distinguished well ( ∼30% overlapped) and many Rel-Far pairs lie farther than Irr-Near pairs.
Learning by LDE can achieve only a marginal improvement (Fig. 4(b)). By contrast, our RDE
achieves a significant improvement in the separability between matching and non-matching pairs,
especially two challenging subsets, Rel-Far and Irr-Near (Fig. 4(c)). Fig. 1 and 2 also show the
superiority of our method over the existing work.
3
References
[1] G. Hua, M. Brown, and S. Winder, “Discriminant embedding for local image descriptors,” in Proceedings
of the International Conference on Computer Vision (ICCV), 2007, pp. 1–8.
[2] D. G. Lowe, “Object recognition from local scale-invariant features,” in Proceedings of the International
Conference on Computer Vision (ICCV), 1999, pp. 1150–1157.
[3] J. Philbin, M. Isard, J. Sivic, and A. Zisserman, “Descriptor learning for efficient retrieval,” inProceedings
of the European Conference on Computer Vision (ECCV), 2010, pp. 677–691.
[4] M. Sugiyama, “Dimensionality reduction of multimodal labeled data by local Fisher discriminant analysis,”
Journal of Machine Learning Research, vol. 5, pp. 1027–1061, 2007.
4
|
Kye-Hyeon Kim, Rui Cai, Lei Zhang, Seungjin Choi
|
Unknown
| 2,013
|
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|
[Review]:
We sincerely appreciate all the reviewers for their time and comments to this manuscript.
We fully agree that it is really hard to find maningful contributions from this short paper, while we tried our best to emphasize them. As we have noted, the full version of this manuscript is currently under review in an international journal. In order to avoid violating the dual-submission policy of the journal, we could not include most of the details and empirical results - only the main idea and some simple examples could be remained in this workshop track submission.
We promise that all the details omitted in this version will be presented clearly in the workshop, e.g., the choice of the weighting of each split, the training dataset used in our experiments, and conclusive empirical comparisons.
For example, we compared the image retrieval performance for landmark buildings in Oxford (http://www.robots.ox.ac.uk/~vgg/data/oxbuildings/) and Paris (http://www.robots.ox.ac.uk/~vgg/data/parisbuildings/). A nonlinear variant of LFDA implemented using deep belief networks (DBN) and a kernelized version of LDE (KDE) were compared to our method. In terms of the mean average precision (mAP) score, we observed significant improvements using our method (mAP: 0.678 on Oxford / 0.700 on Paris) over raw SIFT (0.611 / 0.649), KDE (0.656 / 0.673), DBN (0.662 / 0.678), under the same number of the learned features and the same size of visual vocabulary.
Thanks to all the reviewers again.
|
Kye-Hyeon Kim, Rui Cai, Lei Zhang, Seungjin Choi
| null | null |
{"id": "Xf5Pf5SWhtEYT", "original": null, "cdate": null, "pdate": null, "odate": null, "mdate": null, "tcdate": 1363779180000, "tmdate": 1363779180000, "ddate": null, "number": 3, "content": {"title": "", "review": "We sincerely appreciate all the reviewers for their time and comments to this manuscript.\r\nWe fully agree that it is really hard to find maningful contributions from this short paper, while we tried our best to emphasize them. As we have noted, the full version of this manuscript is currently under review in an international journal. In order to avoid violating the dual-submission policy of the journal, we could not include most of the details and empirical results - only the main idea and some simple examples could be remained in this workshop track submission.\r\n\r\nWe promise that all the details omitted in this version will be presented clearly in the workshop, e.g., the choice of the weighting of each split, the training dataset used in our experiments, and conclusive empirical comparisons.\r\nFor example, we compared the image retrieval performance for landmark buildings in Oxford (http://www.robots.ox.ac.uk/~vgg/data/oxbuildings/) and Paris (http://www.robots.ox.ac.uk/~vgg/data/parisbuildings/). A nonlinear variant of LFDA implemented using deep belief networks (DBN) and a kernelized version of LDE (KDE) were compared to our method. In terms of the mean average precision (mAP) score, we observed significant improvements using our method (mAP: 0.678 on Oxford / 0.700 on Paris) over raw SIFT (0.611 / 0.649), KDE (0.656 / 0.673), DBN (0.662 / 0.678), under the same number of the learned features and the same size of visual vocabulary.\r\n\r\nThanks to all the reviewers again."}, "forum": "zzKhQhsTYlzAZ", "referent": null, "invitation": "ICLR.cc/2013/-/submission/review", "replyto": "zzKhQhsTYlzAZ", "readers": ["everyone"], "nonreaders": [], "signatures": ["Kye-Hyeon Kim, Rui Cai, Lei Zhang, Seungjin Choi"], "writers": ["anonymous"]}
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zzKhQhsTYlzAZ
|
Regularized Discriminant Embedding for Visual Descriptor Learning
|
Images can vary according to changes in viewpoint, resolution, noise, and illumination. In this paper, we aim to learn representations for an image, which are robust to wide changes in such environmental conditions, using training pairs of matching and non-matching local image patches that are collected under various environmental conditions. We present a regularized discriminant analysis that emphasizes two challenging categories among the given training pairs: (1) matching, but far apart pairs and (2) non-matching, but close pairs in the original feature space (e.g., SIFT feature space). Compared to existing work on metric learning and discriminant analysis, our method can better distinguish relevant images from irrelevant, but look-alike images.
|
Regularized Discriminant Embedding for Visual
Descriptor Learning
Kye-Hyeon Kim,a Rui Cai,b Lei Zhang,b Seungjin Choia∗
a Department of Computer Science, POSTECH, Pohang 790-784, Korea
b Microsoft Research Asia, Beijing 100080, China
fenrir@postech.ac.kr, {ruicai, leizhang}@microsoft.com,
seungjin@postech.ac.kr
Abstract
Images can vary according to changes in viewpoint, resolution, noise, and illu-
mination. In this paper, we aim to learn representations for an image, which are
robust to wide changes in such environmental conditions, using training pairs of
matching and non-matching local image patches that are collected under various
environmental conditions. We present a regularized discriminant analysis that em-
phasizes two challenging categories among the given training pairs: (1) matching,
but far apart pairs and (2) non-matching, but close pairs in the original feature
space (e.g., SIFT feature space). Compared to existing work on metric learning
and discriminant analysis, our method can better distinguish relevant images from
irrelevant, but look-alike images.
1 Introduction
In many computer vision problems, images are compared using their local descriptors. A local
descriptor is a feature vector, representing characteristics of an interesting local partin an image.
Scale-invariant feature transform (SIFT) [2] is popularly used for extracting interesting parts and
their local descriptors from an image. Then comparing two images is done by aggregating pairs
between each local descriptor in one image and its closest local descriptor in another image, whose
pairwise distances are below some threshold. The assumption behind this procedure is that local
descriptors corresponding to the same local part (“matching descriptors”) are usually close enough
in the feature space, whereas local descriptors belonging to different local parts (“non-matching
descriptors”) are far apart.
However, this assumption does not hold when there are significant changes in environmental condi-
tions (e.g., viewpoint, illumination, noise, and resolution) between two images. For the same local
part, varying environment conditions can yield varying local image patches, leading to matching
descriptors far apartin the feature space. On the other hand, for different local parts, their image
patches can look similar to each other in some environmental conditions, leading to non-matching
descriptors close together. Fig. 1 shows some examples: in each triplet, the first two image patches
belong to the same local part but captured under different environment conditions, while the third
patch belongs to a different part but looks similar to the second one, resulting that the SIFT descrip-
tors between non-matching local parts are closer than those between matching parts. Consequently,
comparing two images using their local descriptors cannot be done correctly when their are signifi-
cant differences in environmental conditions between the images. Fig. 2(a) shows the cases.
In this paper, we address this problem by learning more robust representations for local image
patches where matching parts are more similar together than non-matching parts even under widely
varying environmental conditions.
∗The full version of this manuscript is currently under review in an international journal.
1
arXiv:1301.3644v1 [cs.CV] 16 Jan 2013
SIFT: 304
LDE: 336
Ours: 360
SIFT: 213
LDE: 268
Ours: 295
SIFT: 268
LDE: 283
Ours: 301
231
275
425
SIFT: 336
LDE: 371
Ours: 362
>
>
<
246
314
372
>
≈
<
199
264
388
SIFT: 267
LDE: 240
Ours: 257
>
<
<
257
319
405
>
<
<
232
291
335
SIFT: 290
LDE: 305
Ours: 349
>
>
<
221
278
365
>
>
<
Figure 1: Some examples where a local part (center in each triplet) is closer to a non-matching part
(right) than a matching part (left) in terms of the Euclidean distances between their SIFT descriptors.
Using linear discriminant embedding (LDE) [1], non-matching pairs are still closer than matching
pairs in the first three examples. Compared to existing work on metric learning and discriminant
analysis, our learning method focuses more on “far but matching” and “close but non-matching”
training pairs, so that can distinguish look-alike irrelevant parts successfully.
(a) 15 closest SIFT pairs
(b) 15 closest RDE pairs
Figure 2: (a) When two images of the same scene are captured under considerably different con-
ditions, many irrelevant pairs of local parts are chosen as closest pairs in the local feature space,
which may lead to undesirable results of comparison. (b) In our RDE space, matching pairs are
successfully chosen as closest pairs.
2 Proposed Method
In descriptor learning [1, 3], a projection is obtained from training pairs of matching and non-
matching descriptors in order to map given local descriptors (e.g., SIFT) to a new feature space
where matching descriptors are closer to each other and non-matching descriptors are farther from
each other. Traditional techniques for supervised dimensionality reduction, including linear discrim-
inant analysis (LDA) and local Fisher discriminant analysis (LFDA) [4], can be applied to descriptor
learning after a slight modification. For example, linear discriminant embedding (LDE) [1] is come
from LDA with a simple modification for handling pairwise training data.
We propose a regularized learning framework in order to further emphasize (1) matching, but far
apart pairs and (2) non-matching, but look-alike pairs, under wide environmental conditions. First,
we divide given training pairs of local descriptors into four subsets, Relevant-Near (Rel-Near),
Relevant-Far (Rel-Far), Irrelevant-Near (Irr-Near), and Irrelevant-Far (Irr-Far). For example, the
“Irr-Near” subset consists of irrelevant (i.e., non-matching), but near pairs. We define an irrelevant
pair (xi,xj) as “near” ifxi is one of the knearest descriptors1 among all non-matching descriptors
of xj or vice versa. Similarly, a relevant pair (xi,xj) is called “near” if xi is one of knearest de-
scriptors among all matching descriptors of xj. All the other pairs belong to “Irr-Far” or “Rel-Far”.
Then we seek a linear projection T that maximizes the following regularized ratio:
J(T) =
βIN
∑
(i,j)∈PIN
dij(T) +βIF
∑
(i,j)∈PIF
dij(T)
βRN
∑
(i,j)∈PRN
dij(T) +βRF
∑
(i,j)∈PRF
dij(T) , (1)
1In our experiments, setting 1 ≤ k ≤ 10 achieved a reasonable performance improvement.
2
−1 −0.5 0 0.5 1
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
LDE
LFDA
RDE
(a)
−1 −0.5 0 0.5 1
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
LDE
LFDA
RDE (b)
Figure 3: Toy examples of projections learned by LDE, LFDA, and our RDE.
0 100 200 300 400 500 600 7000
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Distance
The number of pairs
Err (Rel vs Irr) = 15.58%
Err (RFar vs INear) = 29.92%
RelNear
IrrFar
IrrNear
RelFar
(a) SIFT feature space
0 100 200 300 400 500 600 7000
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Distance
The number of pairs
Err (Rel vs Irr) = 13.99%
Err (RFar vs INear) = 27.00%
RelNear
IrrFar
IrrNear
RelFar (b) LDE feature space
0 100 200 300 400 500 600 7000
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Distance
The number of pairs
Err (Rel vs Irr) = 8.34%
Err (RFar vs INear) = 16.30%
RelNear
IrrFar
IrrNear
RelFar (c) Our RDE feature space
Figure 4: Distribution of Euclidean distance in a given feature space for each subset of pairs. Err
(Rel vs Irr)measures the proportion of overlapping region between {Rel-Near, Rel-Far}and {Irr-
Near, Irr-Far}, while Err (RFar vs INear)measures the overlap between Rel-Far and Irr-Near. In
our RDE space, non-matching pairs are well distinguished from matching pairs.
where dij(T) denotes the squared distance ||T(xi −xj)||2 between two local descriptors xi and xj
in the projected space, and PRN ,PRF ,PIN ,PIF denote the subsets of Rel-Near, Rel-Far, Irr-Near,
and Irr-Far, respectively. Four regularization constantsβRN ,βRF ,βIN ,βIF control the importance
of each subset.
• In LDE, all pairs are equally important, i.e., βRN = βRF = βIN = βIF = 1.
• In LFDA , “near” pairs are more important, i.e.,βRN ≫βRF and βIN ≫βIF .
• In our method, we propose to emphasize Rel-Far (matching but far apart) and Irr-Near
(non-matching but close) pairs, i.e., βRN ≪βRF and βIN ≫βIF .
Fig. 3 shows when and why our method can better distinguish Irr-Near pairs from Rel-Far pairs.
In Fig. 3(a), the global intra-class distribution forms a diagonal, while each local cluster has no
meaningful direction of scattering. Since LFDA focuses on “near” pairs, it cannot capture the true
intra-class scatter well, leading to the undesirable projection. In Fig. 3(b), LDE obtains a projection
that maximizes the inter-class variance, but the shape of the class boundary cannot be considered
well, leading to an overlap between two classes. In this case, focusing more on Irr-Near pairs (i.e.,
the pairs of opposite clusters near the class boundary) can preserve the separability of classes.
Fig. 4 shows the distance distribution of local descriptors, where 20,000 pairs of each subset are
randomly chosen from 500,000 local patches of Flickr images. As shown in Fig. 4(a), Rel-Near
and Irr-Far pairs are already well separated in the SIFT space, but Rel-Far and Irr-Near pairs are
not distinguished well ( ∼30% overlapped) and many Rel-Far pairs lie farther than Irr-Near pairs.
Learning by LDE can achieve only a marginal improvement (Fig. 4(b)). By contrast, our RDE
achieves a significant improvement in the separability between matching and non-matching pairs,
especially two challenging subsets, Rel-Far and Irr-Near (Fig. 4(c)). Fig. 1 and 2 also show the
superiority of our method over the existing work.
3
References
[1] G. Hua, M. Brown, and S. Winder, “Discriminant embedding for local image descriptors,” in Proceedings
of the International Conference on Computer Vision (ICCV), 2007, pp. 1–8.
[2] D. G. Lowe, “Object recognition from local scale-invariant features,” in Proceedings of the International
Conference on Computer Vision (ICCV), 1999, pp. 1150–1157.
[3] J. Philbin, M. Isard, J. Sivic, and A. Zisserman, “Descriptor learning for efficient retrieval,” inProceedings
of the European Conference on Computer Vision (ECCV), 2010, pp. 677–691.
[4] M. Sugiyama, “Dimensionality reduction of multimodal labeled data by local Fisher discriminant analysis,”
Journal of Machine Learning Research, vol. 5, pp. 1027–1061, 2007.
4
|
Kye-Hyeon Kim, Rui Cai, Lei Zhang, Seungjin Choi
|
Unknown
| 2,013
|
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|
[Review]:
The paper aims to present a method for discriminant analysis for image
descriptors. The formulation splits a given dataset of labeled images
into 4 categories, Relevant/Irrelevant and Near/Far pairs
(RN,RF,IN,IF). The final form of the objective aims to maximize the
ratio of sum of distances of irrelevant pairs divided by relevant pairs. The distance metric is calculated at the lower dimensional projected space. The
main contribution of this work as suggested in the paper is selecting
the weighting of 4 splits differently from previous work.
The main intuition or reasoning behind this choice is not given,
neither any conclusive emprical evidence. In the only experiment that
contains real images in the paper, data is said to be taken from
Flickr. However, it is not clear if this is a publicly available
dataset or some random images that authors collected. Moreover, for
this experiment, one of the only two relevant methods are not included
for comparison. Neither, any details of the training procedure nor the actual hyper parameters (eta) are explained in the paper.
|
anonymous reviewer 1e7c
| null | null |
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zzKhQhsTYlzAZ
|
Regularized Discriminant Embedding for Visual Descriptor Learning
|
Images can vary according to changes in viewpoint, resolution, noise, and illumination. In this paper, we aim to learn representations for an image, which are robust to wide changes in such environmental conditions, using training pairs of matching and non-matching local image patches that are collected under various environmental conditions. We present a regularized discriminant analysis that emphasizes two challenging categories among the given training pairs: (1) matching, but far apart pairs and (2) non-matching, but close pairs in the original feature space (e.g., SIFT feature space). Compared to existing work on metric learning and discriminant analysis, our method can better distinguish relevant images from irrelevant, but look-alike images.
|
Regularized Discriminant Embedding for Visual
Descriptor Learning
Kye-Hyeon Kim,a Rui Cai,b Lei Zhang,b Seungjin Choia∗
a Department of Computer Science, POSTECH, Pohang 790-784, Korea
b Microsoft Research Asia, Beijing 100080, China
fenrir@postech.ac.kr, {ruicai, leizhang}@microsoft.com,
seungjin@postech.ac.kr
Abstract
Images can vary according to changes in viewpoint, resolution, noise, and illu-
mination. In this paper, we aim to learn representations for an image, which are
robust to wide changes in such environmental conditions, using training pairs of
matching and non-matching local image patches that are collected under various
environmental conditions. We present a regularized discriminant analysis that em-
phasizes two challenging categories among the given training pairs: (1) matching,
but far apart pairs and (2) non-matching, but close pairs in the original feature
space (e.g., SIFT feature space). Compared to existing work on metric learning
and discriminant analysis, our method can better distinguish relevant images from
irrelevant, but look-alike images.
1 Introduction
In many computer vision problems, images are compared using their local descriptors. A local
descriptor is a feature vector, representing characteristics of an interesting local partin an image.
Scale-invariant feature transform (SIFT) [2] is popularly used for extracting interesting parts and
their local descriptors from an image. Then comparing two images is done by aggregating pairs
between each local descriptor in one image and its closest local descriptor in another image, whose
pairwise distances are below some threshold. The assumption behind this procedure is that local
descriptors corresponding to the same local part (“matching descriptors”) are usually close enough
in the feature space, whereas local descriptors belonging to different local parts (“non-matching
descriptors”) are far apart.
However, this assumption does not hold when there are significant changes in environmental condi-
tions (e.g., viewpoint, illumination, noise, and resolution) between two images. For the same local
part, varying environment conditions can yield varying local image patches, leading to matching
descriptors far apartin the feature space. On the other hand, for different local parts, their image
patches can look similar to each other in some environmental conditions, leading to non-matching
descriptors close together. Fig. 1 shows some examples: in each triplet, the first two image patches
belong to the same local part but captured under different environment conditions, while the third
patch belongs to a different part but looks similar to the second one, resulting that the SIFT descrip-
tors between non-matching local parts are closer than those between matching parts. Consequently,
comparing two images using their local descriptors cannot be done correctly when their are signifi-
cant differences in environmental conditions between the images. Fig. 2(a) shows the cases.
In this paper, we address this problem by learning more robust representations for local image
patches where matching parts are more similar together than non-matching parts even under widely
varying environmental conditions.
∗The full version of this manuscript is currently under review in an international journal.
1
arXiv:1301.3644v1 [cs.CV] 16 Jan 2013
SIFT: 304
LDE: 336
Ours: 360
SIFT: 213
LDE: 268
Ours: 295
SIFT: 268
LDE: 283
Ours: 301
231
275
425
SIFT: 336
LDE: 371
Ours: 362
>
>
<
246
314
372
>
≈
<
199
264
388
SIFT: 267
LDE: 240
Ours: 257
>
<
<
257
319
405
>
<
<
232
291
335
SIFT: 290
LDE: 305
Ours: 349
>
>
<
221
278
365
>
>
<
Figure 1: Some examples where a local part (center in each triplet) is closer to a non-matching part
(right) than a matching part (left) in terms of the Euclidean distances between their SIFT descriptors.
Using linear discriminant embedding (LDE) [1], non-matching pairs are still closer than matching
pairs in the first three examples. Compared to existing work on metric learning and discriminant
analysis, our learning method focuses more on “far but matching” and “close but non-matching”
training pairs, so that can distinguish look-alike irrelevant parts successfully.
(a) 15 closest SIFT pairs
(b) 15 closest RDE pairs
Figure 2: (a) When two images of the same scene are captured under considerably different con-
ditions, many irrelevant pairs of local parts are chosen as closest pairs in the local feature space,
which may lead to undesirable results of comparison. (b) In our RDE space, matching pairs are
successfully chosen as closest pairs.
2 Proposed Method
In descriptor learning [1, 3], a projection is obtained from training pairs of matching and non-
matching descriptors in order to map given local descriptors (e.g., SIFT) to a new feature space
where matching descriptors are closer to each other and non-matching descriptors are farther from
each other. Traditional techniques for supervised dimensionality reduction, including linear discrim-
inant analysis (LDA) and local Fisher discriminant analysis (LFDA) [4], can be applied to descriptor
learning after a slight modification. For example, linear discriminant embedding (LDE) [1] is come
from LDA with a simple modification for handling pairwise training data.
We propose a regularized learning framework in order to further emphasize (1) matching, but far
apart pairs and (2) non-matching, but look-alike pairs, under wide environmental conditions. First,
we divide given training pairs of local descriptors into four subsets, Relevant-Near (Rel-Near),
Relevant-Far (Rel-Far), Irrelevant-Near (Irr-Near), and Irrelevant-Far (Irr-Far). For example, the
“Irr-Near” subset consists of irrelevant (i.e., non-matching), but near pairs. We define an irrelevant
pair (xi,xj) as “near” ifxi is one of the knearest descriptors1 among all non-matching descriptors
of xj or vice versa. Similarly, a relevant pair (xi,xj) is called “near” if xi is one of knearest de-
scriptors among all matching descriptors of xj. All the other pairs belong to “Irr-Far” or “Rel-Far”.
Then we seek a linear projection T that maximizes the following regularized ratio:
J(T) =
βIN
∑
(i,j)∈PIN
dij(T) +βIF
∑
(i,j)∈PIF
dij(T)
βRN
∑
(i,j)∈PRN
dij(T) +βRF
∑
(i,j)∈PRF
dij(T) , (1)
1In our experiments, setting 1 ≤ k ≤ 10 achieved a reasonable performance improvement.
2
−1 −0.5 0 0.5 1
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
LDE
LFDA
RDE
(a)
−1 −0.5 0 0.5 1
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
LDE
LFDA
RDE (b)
Figure 3: Toy examples of projections learned by LDE, LFDA, and our RDE.
0 100 200 300 400 500 600 7000
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Distance
The number of pairs
Err (Rel vs Irr) = 15.58%
Err (RFar vs INear) = 29.92%
RelNear
IrrFar
IrrNear
RelFar
(a) SIFT feature space
0 100 200 300 400 500 600 7000
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Distance
The number of pairs
Err (Rel vs Irr) = 13.99%
Err (RFar vs INear) = 27.00%
RelNear
IrrFar
IrrNear
RelFar (b) LDE feature space
0 100 200 300 400 500 600 7000
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Distance
The number of pairs
Err (Rel vs Irr) = 8.34%
Err (RFar vs INear) = 16.30%
RelNear
IrrFar
IrrNear
RelFar (c) Our RDE feature space
Figure 4: Distribution of Euclidean distance in a given feature space for each subset of pairs. Err
(Rel vs Irr)measures the proportion of overlapping region between {Rel-Near, Rel-Far}and {Irr-
Near, Irr-Far}, while Err (RFar vs INear)measures the overlap between Rel-Far and Irr-Near. In
our RDE space, non-matching pairs are well distinguished from matching pairs.
where dij(T) denotes the squared distance ||T(xi −xj)||2 between two local descriptors xi and xj
in the projected space, and PRN ,PRF ,PIN ,PIF denote the subsets of Rel-Near, Rel-Far, Irr-Near,
and Irr-Far, respectively. Four regularization constantsβRN ,βRF ,βIN ,βIF control the importance
of each subset.
• In LDE, all pairs are equally important, i.e., βRN = βRF = βIN = βIF = 1.
• In LFDA , “near” pairs are more important, i.e.,βRN ≫βRF and βIN ≫βIF .
• In our method, we propose to emphasize Rel-Far (matching but far apart) and Irr-Near
(non-matching but close) pairs, i.e., βRN ≪βRF and βIN ≫βIF .
Fig. 3 shows when and why our method can better distinguish Irr-Near pairs from Rel-Far pairs.
In Fig. 3(a), the global intra-class distribution forms a diagonal, while each local cluster has no
meaningful direction of scattering. Since LFDA focuses on “near” pairs, it cannot capture the true
intra-class scatter well, leading to the undesirable projection. In Fig. 3(b), LDE obtains a projection
that maximizes the inter-class variance, but the shape of the class boundary cannot be considered
well, leading to an overlap between two classes. In this case, focusing more on Irr-Near pairs (i.e.,
the pairs of opposite clusters near the class boundary) can preserve the separability of classes.
Fig. 4 shows the distance distribution of local descriptors, where 20,000 pairs of each subset are
randomly chosen from 500,000 local patches of Flickr images. As shown in Fig. 4(a), Rel-Near
and Irr-Far pairs are already well separated in the SIFT space, but Rel-Far and Irr-Near pairs are
not distinguished well ( ∼30% overlapped) and many Rel-Far pairs lie farther than Irr-Near pairs.
Learning by LDE can achieve only a marginal improvement (Fig. 4(b)). By contrast, our RDE
achieves a significant improvement in the separability between matching and non-matching pairs,
especially two challenging subsets, Rel-Far and Irr-Near (Fig. 4(c)). Fig. 1 and 2 also show the
superiority of our method over the existing work.
3
References
[1] G. Hua, M. Brown, and S. Winder, “Discriminant embedding for local image descriptors,” in Proceedings
of the International Conference on Computer Vision (ICCV), 2007, pp. 1–8.
[2] D. G. Lowe, “Object recognition from local scale-invariant features,” in Proceedings of the International
Conference on Computer Vision (ICCV), 1999, pp. 1150–1157.
[3] J. Philbin, M. Isard, J. Sivic, and A. Zisserman, “Descriptor learning for efficient retrieval,” inProceedings
of the European Conference on Computer Vision (ECCV), 2010, pp. 677–691.
[4] M. Sugiyama, “Dimensionality reduction of multimodal labeled data by local Fisher discriminant analysis,”
Journal of Machine Learning Research, vol. 5, pp. 1027–1061, 2007.
4
|
Kye-Hyeon Kim, Rui Cai, Lei Zhang, Seungjin Choi
|
Unknown
| 2,013
|
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|
[Review]:
This paper describes a method for learning visual feature descriptors that are invariant to changes in illumination, viewpoint, and image quality. The method can be used for multi-view matching and alignment, or for robust image retrieval. The method computes a regularized linear projection of SIFT feature descriptors to optimize a weighted similarity measure. The method is applied to matching and non-matching patches from Flickr images. The primary contribution of this workshop submission is to demonstrate that a coarse weighting of the data samples according to the disparity between their semantic distance and their Euclidean distance in SIFT descriptor space.
The novelty of the paper is minimal, and most details of the method and the validation are not given. The authors focus on the weighting of the sample pairs to emphasize both the furthest similar pairs and the closest dissimilar pairs, but it is not clear that this is provides a substantial gain.
|
anonymous reviewer 39f1
| null | null |
{"id": "-7pc74mqcO-Mr", "original": null, "cdate": null, "pdate": null, "odate": null, "mdate": null, "tcdate": 1362186780000, "tmdate": 1362186780000, "ddate": null, "number": 2, "content": {"title": "review of Regularized Discriminant Embedding for Visual Descriptor Learning", "review": "This paper describes a method for learning visual feature descriptors that are invariant to changes in illumination, viewpoint, and image quality. The method can be used for multi-view matching and alignment, or for robust image retrieval. The method computes a regularized linear projection of SIFT feature descriptors to optimize a weighted similarity measure. The method is applied to matching and non-matching patches from Flickr images. The primary contribution of this workshop submission is to demonstrate that a coarse weighting of the data samples according to the disparity between their semantic distance and their Euclidean distance in SIFT descriptor space.\r\n\r\nThe novelty of the paper is minimal, and most details of the method and the validation are not given. The authors focus on the weighting of the sample pairs to emphasize both the furthest similar pairs and the closest dissimilar pairs, but it is not clear that this is provides a substantial gain."}, "forum": "zzKhQhsTYlzAZ", "referent": null, "invitation": "ICLR.cc/2013/-/submission/review", "replyto": "zzKhQhsTYlzAZ", "readers": ["everyone"], "nonreaders": [], "signatures": ["anonymous reviewer 39f1"], "writers": ["anonymous"]}
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iclr2013
|
openreview
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||
zzEf5eKLmAG0o
|
Learning Features with Structure-Adapting Multi-view Exponential Family
Harmoniums
|
We proposea graphical model for multi-view feature extraction that automatically adapts its structure to achieve better representation of data distribution. The proposed model, structure-adapting multi-view harmonium (SA-MVH) has switch parameters that control the connection between hidden nodes and input views, and learn the switch parameter while training. Numerical experiments on synthetic and a real-world dataset demonstrate the useful behavior of the SA-MVH, compared to existing multi-view feature extraction methods.
|
arXiv:1301.3539v1 [cs.LG] 16 Jan 2013
Learning Features with Structure-Adapting
Multi-view Exponential Family Harmoniums
Yoonseop Kang1 Seungjin Choi1,2,3
Department of Computer Science and Engineering1,
Division of IT Convergence Engineering2,
Department of Creative Excellence Engineering3,
Pohang University of Science and Technology (POSTECH)
Pohang, South Korea, 790-784.
{e0en,seungjin}@postech.ac.kr
Abstract
We propose a graphical model for multi-view feature extraction that automatically
adapts its structure to achieve better representation of da ta distribution. The pro-
posed model, structure-adapting multi-view harmonium (SA-MVH) has switch
parameters that control the connection between hidden nodes and input v iews,
and learn the switch parameter while training. Numerical ex periments on syn-
thetic and a real-world dataset demonstrate the useful beha vior of the SA-MVH,
compared to existing multi-view feature extraction methods.
1 Introduction
Earlier multi-view feature extraction methods including canonical correlation analysis [1] and dual-
wing harmonium (DWH) [2] assume that all views can be describ ed using a single set of shared
hidden nodes. However, these methods fail when real-world data with partially correlated views are
given. More recent methods like factorized orthogonal late nt space [3] or multi-view harmonium
(MVH) [4] assume that views are generated from two sets of hid den nodes: view-specific hidden
nodes and shared ones. Still, these models rely on the pre-defined connection structure, and deciding
the number of shared and view-specific hidden nodes requires a great human effort.
In this paper, we propose structure-adapting multi-view ha rmonium (SA-MVH) which avoids all
of the problems mentioned above. Instead of explicitly defin ing view-specific and hidden nodes in
prior to the training, we only use one set of hidden nodes and l et each one of them to decide the
existence of connection to views using switch parameters during the training. In this manner, SA-
MVH automatically decides the number of view-specific laten t variables and also captures partial
correlation among views.
2 The Proposed Model
The definition of SA-MVH begins with choosing marginal distr ibutions of visible node sets v(k)
and a set of hidden nodes h from exponential family distributions:
p(v(k)
i ) ∝ exp(
∑
a
ξ(k)
ia f(k)
ia (v(k)
i ) − A(k)
i ({ξ(k)
ia })),
p(hj ) ∝ exp(
∑
b
λjb gjb(hj ) − Bj ({λjb })), (1)
f(·), g(·) are sufficient statistics, ξ, λ are natural parameters, and A, B are log-partition functions.
1
...
... ...
(a) DWH
...
... ...
... ...
(b) MVH
...
... ...
(c) SA-MVH
Figure 1: Graphical models of (a) dual-wing harmonium, (b) m ulti-view harmonium, and (c)
structure-adapting multi-view harmonium.
Connections between visible nodes and hidden nodes of SA-MV H are defined by weight matrices
{W (k)} and switch parameters σ(skj ) ∈ [0, 1], where σ(·) is a sigmoid function. A switch skj
controls the connection between k-th view and j-th hidden node by being multiplied to the j-th
column of weight matrix W (k) (Figure 1). When σ(skj ) is large (> 0. 5), we consider the view and
the hidden node to be connected. With the quadratic term including weights and switch parameters,
the joint distribution of SA-MVH is defined as below:
p({v(k)}, h) ∝ exp
( ∑
k,i,j
σ(skj )W (k)
ij f(k)
i (v(k)
i )gj (hj ) −
∑
k,i
ξ(k)
i f(k)
i (v(k)
i ) −
∑
j
λj gj (hj )
)
. (2)
note that indices a and b are omitted to keep the notations uncluttered.
We learn the parameters W (k), ξ(k), λ, and switch parameters skj by maximizing the likelihood of
model via gradient ascent. The likelihood of SA-MVH is define d as the joint distribution of nodes
summed over hidden nodes h:
L = ⟨log p({v(k)})⟩data =
⟨
log
∑
h
p({v(k)}, h)
⟩
data, (3)
where ⟨·⟩data represents expectation over data distribution. Then the gradient of log-likelihood with
respect to the parameters W (k), ξ(k), λ, and skj are derived as follows:
∂L
∂W (k)
ij
∝
⟨
σ(skj )fi(v(k)
i )B′
j (ˆλj )
⟩
data −
⟨
σ(skj )fi(v(k)
i )B′
j (ˆλj )
⟩
model (4)
∂L
∂ξ(k)
i
∝
⟨
f(k)
i (v(k)
i )
⟩
data −
⟨
f(k)
i (v(k)
i )
⟩
model (5)
∂L
∂λ j
∝
⟨
B′
j (ˆλj )
⟩
data −
⟨
B′
j (ˆλj )
⟩
model, (6)
∂L
∂skj
∝
⣨
σ′(skj )W (k)
ij fi(v(k)
i )B′
j (ˆλj )
⟩
data
−
⣨
σ′(skj )W (k)
ij fi(v(k)
i )B′
j (ˆλj )
⟩
model
(7)
where ⟨·⟩model represents expectation over model distribution p({v(k)}, h) and ˆξ(k)
i = ξ(k)
i +∑
j σ(skj )W (k)
ij gj(hj ), ˆλj = λj + ∑
k,i σ(skj )W (k)
ij fi(v(k)
i ) are shifted parameters.
3 Numerical Experiments
3.1 Feature Extraction on Noisy Arabic-Roman Digit Dataset
To simulate the view-specific and shared properties of multi -view data, we designed a synthetic
dataset which contains 11,800 pairs of Arabic digits and the corresponding Roman digits written in
various fonts. For each pair, we added random vertical line n oises to Arabic digits, and horizontal
line noises to Roman digits (Figure 2-(a)). SA-MVH trained with 200 hidden nodes found 95 shared
features (with connection to both views), and 47 view-speci fic features for Roman digits, and 32
for Arabic digits. Remaining 26 were not connected to any vie ws and ignored. Most of the shared
features were noise-free and encoded parts of Roman and Arab ic numbers (Figure 2-(b)). On the
other hand, the view-specific features had components with horizontal or vertical noises, as well as
the parts of the numbers (Figure 2-(c)). In this example, SA- MVH automatically separated view-
specific and shared information without any prior specification of the graph structure.
2
(a)
(b) Shared features
(c) View-specific features
Figure 2: (a) 10 samples from Noisy Arabic-Roman digit dataset, (b) shared features, and (c) view-
specific features learned by SA-MVH.
Table 1: Image classification accuracy of k-nn classifier using feature extraction methods trained on
Caltech-256 dataset. For each value of k, the best result is marked as bold text.
Method # 10-NN 30-NN 50-NN 70-NN 100-NN
Sparse Filtering 0.161 0.165 0.163 0.16 0.155
DWH 0.237 0.231 0.217 0.207 0.194
MVH 0.239 0.225 0.216 0.203 0.191
SA-MVH 0.246 0.232 0.223 0.212 0.198
3.2 Image Classification on Caltech-256 Dataset
We extracted 512 dimensions of GIST features and 1,536 dimen sions of histogram of gradients
(HoG) features from Caltech-256 dataset to simulate multi-view settings. SA-MVH and other multi-
view feature extraction methods based on harmonium – DWH andMVH were trained on the dataset
for comparison. We also compared our method to Sparse Filter ing [5], which is not a harmonium-
based method. We trained the feature extraction methods and tested the methods with k-nearest
neighbor classifiers (Table 1). SA-MVH resulted better than other feature extraction models in this
experiment, regardless of the value of k for nearest neighbor classifier.
4 Conclusion
In this paper, we have proposed the multi-view feature extraction model that automatically decides
relations between latent variables and input views. The pro posed method, SA-MVH models multi-
view data distribution with less restrictive assumption and also reduces the number of parameters to
tune by human hand. SA-MVH introduces switch parameters that control the connections between
hidden nodes and input views, and find the desirable configuration while training. We have demon-
strated the effectiveness of our approach by comparing our model to existing models in experiments
on synthetic dataset, and image classification with simulated multi-view setting.
References
[1] D. R. Hardoon, S. Szedmak, and J. Shawe-Taylor, “Canonical correlation analysis: An overview
with applications to learning methods,” Neural Computation, vol. 16, pp. 2639–2664, 2004.
[2] E. P. Xing, R. Yan, and A. G. Hauptmann, “Mining associate d text and images with dual-wing
harmonium,” in Proceedings of the Annual Conference on Uncertainty in Artificial Intelligence
(UAI), Edinburgh, UK, 2005.
[3] M. Salzmann, C. H. Ek, R. Urtasun, and T. Darrell, “Factor ized orthogonal latent spaces,” in
Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS),
Sardinia, Italy, 2010.
[4] Y . Kang and S. Choi, “Restricted deep belief networks formulti-view learning,” in Proceedings
of the European Conference on Machine Learning and Principl es and Practice of Knowledge
Discovery in Databases (ECML-PKDD), Athens, Greece, 2011.
[5] J. Ngiam, P. W. Koh, Z. Chen, S. A. Bhaskar, and A. Y . Ng, “Sp arse filtering,” in Advances in
Neural Information Processing Systems (NIPS), vol. 23. MIT Press, 2011.
3
|
YoonSeop Kang, Seungjin Choi
|
Unknown
| 2,013
|
{"id": "zzEf5eKLmAG0o", "original": null, "cdate": null, "pdate": null, "odate": null, "mdate": null, "tcdate": 1358403300000, "tmdate": 1358403300000, "ddate": null, "number": 47, "content": {"title": "Learning Features with Structure-Adapting Multi-view Exponential Family\r\n Harmoniums", "decision": "conferencePoster-iclr2013-workshop", "abstract": "We proposea graphical model for multi-view feature extraction that automatically adapts its structure to achieve better representation of data distribution. The proposed model, structure-adapting multi-view harmonium (SA-MVH) has switch parameters that control the connection between hidden nodes and input views, and learn the switch parameter while training. Numerical experiments on synthetic and a real-world dataset demonstrate the useful behavior of the SA-MVH, compared to existing multi-view feature extraction methods.", "pdf": "https://arxiv.org/abs/1301.3539", "paperhash": "kang|learning_features_with_structureadapting_multiview_exponential_family_harmoniums", "authors": ["YoonSeop Kang", "Seungjin Choi"], "keywords": [], "conflicts": [], "authorids": ["e0engoon@gmail.com", "seungjin.choi.mlg@gmail.com"]}, "forum": "zzEf5eKLmAG0o", "referent": null, "invitation": "ICLR.cc/2013/conference/-/submission", "replyto": null, "readers": ["everyone"], "nonreaders": [], "signatures": ["e0engoon@gmail.com"], "writers": []}
|
[Review]:
The paper introduces an new algorithm for simultaneously learning a hidden layer (latent representation) for multiple data views as well as automatically segmenting that hidden layer into shared and view-specific nodes. It builds on the previous multi-view harmonium (MVH) algorithm by adding (sigmoidal) switch parameters that turn a connection on or off between a view and hidden node and uses gradient descent to learn those switch parameters. The optimization is similar to MVH, with a slight modification on the joint distribution between views and hidden nodes, resulting in a change in the gradients for all parameters and a new switch variable to descend on.
This new algorithm, therefore, is somewhat novel; the quality of the explanation and writing is high; and the experimental quality is reasonable.
Pros
1. The paper is well-written and organized.
2. The algorithm in the paper proposes a way to avoid hand designing shared and private (view-specific) nodes, which is an important contribution.
3. The experimental results indicate some interesting properties of the algorithm, in particular demonstrating that the algorithm extracts reasonable shared and view-specific hidden nodes.
Cons
1. The descent directions have W and the switch parameters, s_kj, coupled, which might make learning slow. Experimental results should indicate computation time.
2. The results do not have error bars (in Table 1), so it is unclear if they are statistically significant (the small difference suggests that they may not be).
3. The motivation in this paper is to enable learning of the private and shared representations automatically. However, DWH (only a shared representation) actually seems to perform generally better that MVH (shared and private). The experiments should better explore this question. It might also be a good idea to have a baseline comparison with CCA.
4. In light of Con (3), the algorithm should also be compared to multi-view algorithms that learn only shared representations but do not require the size of the hidden-node set to be fixed (such as the recent relaxed-rank convex multi-view approach in 'Convex Multiview Subspace Learning', M. White, Y. Yu, X. Zhang and D. Schuurmans, NIPS 2012). In this case, the relaxed-rank regularizer does not fix the size of the hidden node set, but regularizes to set several hidden nodes to zero. This is similar to the approach proposed in this paper where a node is not used if the sigmoid value is < 0.5.
Note that these relaxed-rank approaches do not explicitly maximize the likelihood for an exponential family distribution; instead, they allow general Bregman divergences which have been shown to have a one-to-one correspondence with exponential family distributions (see 'Clustering with Bregman divergences' A. Banerjee, S. Merugu, I. Dhillon and J. Ghosh, JMLR 2005). Therefore, by selecting a certain Bregman divergence, the approach in this paper can be compared to the relaxed-rank approaches.
|
anonymous reviewer d966
| null | null |
{"id": "UUlHmZjBOIUBb", "original": null, "cdate": null, "pdate": null, "odate": null, "mdate": null, "tcdate": 1362353160000, "tmdate": 1362353160000, "ddate": null, "number": 2, "content": {"title": "review of Learning Features with Structure-Adapting Multi-view Exponential Family\r\n Harmoniums", "review": "The paper introduces an new algorithm for simultaneously learning a hidden layer (latent representation) for multiple data views as well as automatically segmenting that hidden layer into shared and view-specific nodes. It builds on the previous multi-view harmonium (MVH) algorithm by adding (sigmoidal) switch parameters that turn a connection on or off between a view and hidden node and uses gradient descent to learn those switch parameters. The optimization is similar to MVH, with a slight modification on the joint distribution between views and hidden nodes, resulting in a change in the gradients for all parameters and a new switch variable to descend on.\r\n\r\nThis new algorithm, therefore, is somewhat novel; the quality of the explanation and writing is high; and the experimental quality is reasonable.\r\n\r\nPros\r\n\r\n1. The paper is well-written and organized.\r\n\r\n2. The algorithm in the paper proposes a way to avoid hand designing shared and private (view-specific) nodes, which is an important contribution.\r\n\r\n3. The experimental results indicate some interesting properties of the algorithm, in particular demonstrating that the algorithm extracts reasonable shared and view-specific hidden nodes.\r\n\r\nCons\r\n1. The descent directions have W and the switch parameters, s_kj, coupled, which might make learning slow. Experimental results should indicate computation time.\r\n\r\n2. The results do not have error bars (in Table 1), so it is unclear if they are statistically significant (the small difference suggests that they may not be).\r\n\r\n3. The motivation in this paper is to enable learning of the private and shared representations automatically. However, DWH (only a shared representation) actually seems to perform generally better that MVH (shared and private). The experiments should better explore this question. It might also be a good idea to have a baseline comparison with CCA. \r\n\r\n4. In light of Con (3), the algorithm should also be compared to multi-view algorithms that learn only shared representations but do not require the size of the hidden-node set to be fixed (such as the recent relaxed-rank convex multi-view approach in 'Convex Multiview Subspace Learning', M. White, Y. Yu, X. Zhang and D. Schuurmans, NIPS 2012). In this case, the relaxed-rank regularizer does not fix the size of the hidden node set, but regularizes to set several hidden nodes to zero. This is similar to the approach proposed in this paper where a node is not used if the sigmoid value is < 0.5. \r\nNote that these relaxed-rank approaches do not explicitly maximize the likelihood for an exponential family distribution; instead, they allow general Bregman divergences which have been shown to have a one-to-one correspondence with exponential family distributions (see 'Clustering with Bregman divergences' A. Banerjee, S. Merugu, I. Dhillon and J. Ghosh, JMLR 2005). Therefore, by selecting a certain Bregman divergence, the approach in this paper can be compared to the relaxed-rank approaches."}, "forum": "zzEf5eKLmAG0o", "referent": null, "invitation": "ICLR.cc/2013/-/submission/review", "replyto": "zzEf5eKLmAG0o", "readers": ["everyone"], "nonreaders": [], "signatures": ["anonymous reviewer d966"], "writers": ["anonymous"]}
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zzEf5eKLmAG0o
|
Learning Features with Structure-Adapting Multi-view Exponential Family
Harmoniums
|
We proposea graphical model for multi-view feature extraction that automatically adapts its structure to achieve better representation of data distribution. The proposed model, structure-adapting multi-view harmonium (SA-MVH) has switch parameters that control the connection between hidden nodes and input views, and learn the switch parameter while training. Numerical experiments on synthetic and a real-world dataset demonstrate the useful behavior of the SA-MVH, compared to existing multi-view feature extraction methods.
|
arXiv:1301.3539v1 [cs.LG] 16 Jan 2013
Learning Features with Structure-Adapting
Multi-view Exponential Family Harmoniums
Yoonseop Kang1 Seungjin Choi1,2,3
Department of Computer Science and Engineering1,
Division of IT Convergence Engineering2,
Department of Creative Excellence Engineering3,
Pohang University of Science and Technology (POSTECH)
Pohang, South Korea, 790-784.
{e0en,seungjin}@postech.ac.kr
Abstract
We propose a graphical model for multi-view feature extraction that automatically
adapts its structure to achieve better representation of da ta distribution. The pro-
posed model, structure-adapting multi-view harmonium (SA-MVH) has switch
parameters that control the connection between hidden nodes and input v iews,
and learn the switch parameter while training. Numerical ex periments on syn-
thetic and a real-world dataset demonstrate the useful beha vior of the SA-MVH,
compared to existing multi-view feature extraction methods.
1 Introduction
Earlier multi-view feature extraction methods including canonical correlation analysis [1] and dual-
wing harmonium (DWH) [2] assume that all views can be describ ed using a single set of shared
hidden nodes. However, these methods fail when real-world data with partially correlated views are
given. More recent methods like factorized orthogonal late nt space [3] or multi-view harmonium
(MVH) [4] assume that views are generated from two sets of hid den nodes: view-specific hidden
nodes and shared ones. Still, these models rely on the pre-defined connection structure, and deciding
the number of shared and view-specific hidden nodes requires a great human effort.
In this paper, we propose structure-adapting multi-view ha rmonium (SA-MVH) which avoids all
of the problems mentioned above. Instead of explicitly defin ing view-specific and hidden nodes in
prior to the training, we only use one set of hidden nodes and l et each one of them to decide the
existence of connection to views using switch parameters during the training. In this manner, SA-
MVH automatically decides the number of view-specific laten t variables and also captures partial
correlation among views.
2 The Proposed Model
The definition of SA-MVH begins with choosing marginal distr ibutions of visible node sets v(k)
and a set of hidden nodes h from exponential family distributions:
p(v(k)
i ) ∝ exp(
∑
a
ξ(k)
ia f(k)
ia (v(k)
i ) − A(k)
i ({ξ(k)
ia })),
p(hj ) ∝ exp(
∑
b
λjb gjb(hj ) − Bj ({λjb })), (1)
f(·), g(·) are sufficient statistics, ξ, λ are natural parameters, and A, B are log-partition functions.
1
...
... ...
(a) DWH
...
... ...
... ...
(b) MVH
...
... ...
(c) SA-MVH
Figure 1: Graphical models of (a) dual-wing harmonium, (b) m ulti-view harmonium, and (c)
structure-adapting multi-view harmonium.
Connections between visible nodes and hidden nodes of SA-MV H are defined by weight matrices
{W (k)} and switch parameters σ(skj ) ∈ [0, 1], where σ(·) is a sigmoid function. A switch skj
controls the connection between k-th view and j-th hidden node by being multiplied to the j-th
column of weight matrix W (k) (Figure 1). When σ(skj ) is large (> 0. 5), we consider the view and
the hidden node to be connected. With the quadratic term including weights and switch parameters,
the joint distribution of SA-MVH is defined as below:
p({v(k)}, h) ∝ exp
( ∑
k,i,j
σ(skj )W (k)
ij f(k)
i (v(k)
i )gj (hj ) −
∑
k,i
ξ(k)
i f(k)
i (v(k)
i ) −
∑
j
λj gj (hj )
)
. (2)
note that indices a and b are omitted to keep the notations uncluttered.
We learn the parameters W (k), ξ(k), λ, and switch parameters skj by maximizing the likelihood of
model via gradient ascent. The likelihood of SA-MVH is define d as the joint distribution of nodes
summed over hidden nodes h:
L = ⟨log p({v(k)})⟩data =
⟨
log
∑
h
p({v(k)}, h)
⟩
data, (3)
where ⟨·⟩data represents expectation over data distribution. Then the gradient of log-likelihood with
respect to the parameters W (k), ξ(k), λ, and skj are derived as follows:
∂L
∂W (k)
ij
∝
⟨
σ(skj )fi(v(k)
i )B′
j (ˆλj )
⟩
data −
⟨
σ(skj )fi(v(k)
i )B′
j (ˆλj )
⟩
model (4)
∂L
∂ξ(k)
i
∝
⟨
f(k)
i (v(k)
i )
⟩
data −
⟨
f(k)
i (v(k)
i )
⟩
model (5)
∂L
∂λ j
∝
⟨
B′
j (ˆλj )
⟩
data −
⟨
B′
j (ˆλj )
⟩
model, (6)
∂L
∂skj
∝
⣨
σ′(skj )W (k)
ij fi(v(k)
i )B′
j (ˆλj )
⟩
data
−
⣨
σ′(skj )W (k)
ij fi(v(k)
i )B′
j (ˆλj )
⟩
model
(7)
where ⟨·⟩model represents expectation over model distribution p({v(k)}, h) and ˆξ(k)
i = ξ(k)
i +∑
j σ(skj )W (k)
ij gj(hj ), ˆλj = λj + ∑
k,i σ(skj )W (k)
ij fi(v(k)
i ) are shifted parameters.
3 Numerical Experiments
3.1 Feature Extraction on Noisy Arabic-Roman Digit Dataset
To simulate the view-specific and shared properties of multi -view data, we designed a synthetic
dataset which contains 11,800 pairs of Arabic digits and the corresponding Roman digits written in
various fonts. For each pair, we added random vertical line n oises to Arabic digits, and horizontal
line noises to Roman digits (Figure 2-(a)). SA-MVH trained with 200 hidden nodes found 95 shared
features (with connection to both views), and 47 view-speci fic features for Roman digits, and 32
for Arabic digits. Remaining 26 were not connected to any vie ws and ignored. Most of the shared
features were noise-free and encoded parts of Roman and Arab ic numbers (Figure 2-(b)). On the
other hand, the view-specific features had components with horizontal or vertical noises, as well as
the parts of the numbers (Figure 2-(c)). In this example, SA- MVH automatically separated view-
specific and shared information without any prior specification of the graph structure.
2
(a)
(b) Shared features
(c) View-specific features
Figure 2: (a) 10 samples from Noisy Arabic-Roman digit dataset, (b) shared features, and (c) view-
specific features learned by SA-MVH.
Table 1: Image classification accuracy of k-nn classifier using feature extraction methods trained on
Caltech-256 dataset. For each value of k, the best result is marked as bold text.
Method # 10-NN 30-NN 50-NN 70-NN 100-NN
Sparse Filtering 0.161 0.165 0.163 0.16 0.155
DWH 0.237 0.231 0.217 0.207 0.194
MVH 0.239 0.225 0.216 0.203 0.191
SA-MVH 0.246 0.232 0.223 0.212 0.198
3.2 Image Classification on Caltech-256 Dataset
We extracted 512 dimensions of GIST features and 1,536 dimen sions of histogram of gradients
(HoG) features from Caltech-256 dataset to simulate multi-view settings. SA-MVH and other multi-
view feature extraction methods based on harmonium – DWH andMVH were trained on the dataset
for comparison. We also compared our method to Sparse Filter ing [5], which is not a harmonium-
based method. We trained the feature extraction methods and tested the methods with k-nearest
neighbor classifiers (Table 1). SA-MVH resulted better than other feature extraction models in this
experiment, regardless of the value of k for nearest neighbor classifier.
4 Conclusion
In this paper, we have proposed the multi-view feature extraction model that automatically decides
relations between latent variables and input views. The pro posed method, SA-MVH models multi-
view data distribution with less restrictive assumption and also reduces the number of parameters to
tune by human hand. SA-MVH introduces switch parameters that control the connections between
hidden nodes and input views, and find the desirable configuration while training. We have demon-
strated the effectiveness of our approach by comparing our model to existing models in experiments
on synthetic dataset, and image classification with simulated multi-view setting.
References
[1] D. R. Hardoon, S. Szedmak, and J. Shawe-Taylor, “Canonical correlation analysis: An overview
with applications to learning methods,” Neural Computation, vol. 16, pp. 2639–2664, 2004.
[2] E. P. Xing, R. Yan, and A. G. Hauptmann, “Mining associate d text and images with dual-wing
harmonium,” in Proceedings of the Annual Conference on Uncertainty in Artificial Intelligence
(UAI), Edinburgh, UK, 2005.
[3] M. Salzmann, C. H. Ek, R. Urtasun, and T. Darrell, “Factor ized orthogonal latent spaces,” in
Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS),
Sardinia, Italy, 2010.
[4] Y . Kang and S. Choi, “Restricted deep belief networks formulti-view learning,” in Proceedings
of the European Conference on Machine Learning and Principl es and Practice of Knowledge
Discovery in Databases (ECML-PKDD), Athens, Greece, 2011.
[5] J. Ngiam, P. W. Koh, Z. Chen, S. A. Bhaskar, and A. Y . Ng, “Sp arse filtering,” in Advances in
Neural Information Processing Systems (NIPS), vol. 23. MIT Press, 2011.
3
|
YoonSeop Kang, Seungjin Choi
|
Unknown
| 2,013
|
{"id": "zzEf5eKLmAG0o", "original": null, "cdate": null, "pdate": null, "odate": null, "mdate": null, "tcdate": 1358403300000, "tmdate": 1358403300000, "ddate": null, "number": 47, "content": {"title": "Learning Features with Structure-Adapting Multi-view Exponential Family\r\n Harmoniums", "decision": "conferencePoster-iclr2013-workshop", "abstract": "We proposea graphical model for multi-view feature extraction that automatically adapts its structure to achieve better representation of data distribution. The proposed model, structure-adapting multi-view harmonium (SA-MVH) has switch parameters that control the connection between hidden nodes and input views, and learn the switch parameter while training. Numerical experiments on synthetic and a real-world dataset demonstrate the useful behavior of the SA-MVH, compared to existing multi-view feature extraction methods.", "pdf": "https://arxiv.org/abs/1301.3539", "paperhash": "kang|learning_features_with_structureadapting_multiview_exponential_family_harmoniums", "authors": ["YoonSeop Kang", "Seungjin Choi"], "keywords": [], "conflicts": [], "authorids": ["e0engoon@gmail.com", "seungjin.choi.mlg@gmail.com"]}, "forum": "zzEf5eKLmAG0o", "referent": null, "invitation": "ICLR.cc/2013/conference/-/submission", "replyto": null, "readers": ["everyone"], "nonreaders": [], "signatures": ["e0engoon@gmail.com"], "writers": []}
|
[Review]:
The authors propose a bipartite, undirected graphical model for multiview learning, called structure-adapting multiview harmonimum (SA-MVH). The model is based on their earlier model called multiview harmonium (MVH) (Kang&Choi, 2011) where hidden units were separated into a shared set and view-specific sets. Unlike MVH which explicitly restricts edges, the visible and hidden units in the proposed SA-MVH are fully connected to each other with switch parameters s_{kj} indicating how likely the j-th hidden unit corresponds to the k-th view.
It would have been better if the distribution of s_{kj}'s (or sigma(s_{kj})) was provided. Unless the distribution has clear modes near 0 and 1, it would be difficult to tell why this approach of learning w^{(k)}_{ij} and s_{kj} separately is better than just learning ilde{w}^{(k)}_{ij} = w^{(k)}_{ij} sigma s_{kj} all together (as in dual-wing harmonium, DWH). Though, the empirical results (experiment 2) show that the features extracted by SA-MVH outperform both MVH and DWH.
The visualizations of shared and view-specific features from the first experiment do not seem to clearly show the power of the proposed method. For instance, it's difficult to say that the filters of roman digits from the shared features do seem to have horizontal noise. It would be better to try some other tasks with the trained model. Would it be possible to sample clean digits (without horizontal or vertical noise) from the model if the view-speific features were forced off? Would it be possible to denoise the corrupted digits? and so on..
Typo:
- Fig. 1 (c): sigma(s_{1j}) and sigma(s_{2j})
|
anonymous reviewer 0e7e
| null | null |
{"id": "DNKnDqeVJmgPF", "original": null, "cdate": null, "pdate": null, "odate": null, "mdate": null, "tcdate": 1360866060000, "tmdate": 1360866060000, "ddate": null, "number": 1, "content": {"title": "review of Learning Features with Structure-Adapting Multi-view Exponential Family\r\n Harmoniums", "review": "The authors propose a bipartite, undirected graphical model for multiview learning, called structure-adapting multiview harmonimum (SA-MVH). The model is based on their earlier model called multiview harmonium (MVH) (Kang&Choi, 2011) where hidden units were separated into a shared set and view-specific sets. Unlike MVH which explicitly restricts edges, the visible and hidden units in the proposed SA-MVH are fully connected to each other with switch parameters s_{kj} indicating how likely the j-th hidden unit corresponds to the k-th view.\r\n\r\nIt would have been better if the distribution of s_{kj}'s (or sigma(s_{kj})) was provided. Unless the distribution has clear modes near 0 and 1, it would be difficult to tell why this approach of learning w^{(k)}_{ij} and s_{kj} separately is better than just learning \tilde{w}^{(k)}_{ij} = w^{(k)}_{ij} sigma s_{kj} all together (as in dual-wing harmonium, DWH). Though, the empirical results (experiment 2) show that the features extracted by SA-MVH outperform both MVH and DWH.\r\n\r\nThe visualizations of shared and view-specific features from the first experiment do not seem to clearly show the power of the proposed method. For instance, it's difficult to say that the filters of roman digits from the shared features do seem to have horizontal noise. It would be better to try some other tasks with the trained model. Would it be possible to sample clean digits (without horizontal or vertical noise) from the model if the view-speific features were forced off? Would it be possible to denoise the corrupted digits? and so on..\r\n\r\nTypo:\r\n\r\n- Fig. 1 (c): sigma(s_{1j}) and sigma(s_{2j})"}, "forum": "zzEf5eKLmAG0o", "referent": null, "invitation": "ICLR.cc/2013/-/submission/review", "replyto": "zzEf5eKLmAG0o", "readers": ["everyone"], "nonreaders": [], "signatures": ["anonymous reviewer 0e7e"], "writers": ["anonymous"]}
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yyC_7RZTkUD5-
|
Deep Predictive Coding Networks
|
The quality of data representation in deep learning methods is directly related to the prior model imposed on the representations; however, generally used fixed priors are not capable of adjusting to the context in the data. To address this issue, we propose deep predictive coding networks, a hierarchical generative model that empirically alters priors on the latent representations in a dynamic and context-sensitive manner. This model captures the temporal dependencies in time-varying signals and uses top-down information to modulate the representation in lower layers. The centerpiece of our model is a novel procedure to infer sparse states of a dynamic model; which is used for feature extraction. We also extend this feature extraction block to introduce a pooling function that captures locally invariant representations. When applied on a natural video data, we show that our method is able to learn high-level visual features. We also demonstrate the role of the top-down connections by showing the robustness of the proposed model to structured noise.
|
arXiv:1301.3541v3 [cs.LG] 15 Mar 2013
Deep Predictive Coding Networks
Rakesh Chalasani Jose C. Principe
Department of Electrical and Computer Engineering
University of Florida, Gainesville, FL 32611
rakeshch@ufl.edu, principe@cnel.ufl.edu
Abstract
The quality of data representation in deep learning methods is directly related to
the prior model imposed on the representations; however, ge nerally used fixed
priors are not capable of adjusting to the context in the data. To address this issue,
we propose deep predictive coding networks, a hierarchical generative model that
empirically alters priors on the latent representations in a dynamic and context-
sensitive manner. This model captures the temporal dependencies in time-varying
signals and uses top-down information to modulate the repre sentation in lower
layers. The centerpiece of our model is a novel procedure to infer sparse states of a
dynamic network which is used for feature extraction. We also extend this feature
extraction block to introduce a pooling function that captu res locally invariant
representations. When applied on a natural video data, we sh ow that our method
is able to learn high-level visual features. We also demonstrate the role of the top-
down connections by showing the robustness of the proposed model to structured
noise.
1 Introduction
The performance of machine learning algorithms is dependen t on how the data is represented. In
most methods, the quality of a data representation is itselfdependent on prior knowledge imposed on
the representation. Such prior knowledge can be imposed usi ng domain specific information, as in
SIFT [1], HOG [2], etc., or in learning representations usin g fixed priors like sparsity [3], temporal
coherence [4], etc. The use of fixed priors became particularly popular while training deep networks
[5–8]. In spite of the success of these general purpose prior s, they are not capable of adjusting to
the context in the data. On the other hand, there are several a dvantages to having a model that can
“actively” adapt to the context in the data. One way of achiev ing this is to empirically alter the
priors in a dynamic and context-sensitive manner. This will be the m ain focus of this work, with
emphasis on visual perception.
Here we propose a predictive coding framework, where a deep locally-connected generative model
uses “top-down” information to empirically alter the prior s used in the lower layers to perform
“bottom-up” inference. The centerpiece of the proposed mod el is extracting sparse features from
time-varying observations using a linear dynamical model . To this end, we propose a novel proce-
dure to infer sparse states (or features) of a dynamical system. We then extend this feature extraction
block to introduce a pooling strategy to learn invariant feature representations from the data. In line
with other “deep learning” methods, we use these basic build ing blocks to construct a hierarchical
model using greedy layer-wise unsupervised learning. The h ierarchical model is built such that the
output from one layer acts as an input to the layer above. In other words, the layers are arranged in a
Markov chain such that the states at any layer are only dependent on the representations in the layer
below and above, and are independent of the rest of the model. The overall goal of the dynamical
system at any layer is to make the best prediction of the representation in the layer below using the
top-down information from the layers above and the temporal information from the previous states.
Hence, the name deep predictive coding networks (DPCN).
1
1.1 Related W ork
The DPCN proposed here is closely related to models proposed in [9, 10], where predictive cod-
ing is used as a statistical model to explain cortical functi ons in the mammalian brain. Similar to
the proposed model, they construct hierarchical generative models that seek to infer the underlying
causes of the sensory inputs. While Rao and Ballard [9] use an update rule similar to Kalman filter
for inference, Friston [10] proposed a general framework considering all the higher-order moments
in a continuous time dynamic model. However, neither of the m odels is capable of extracting dis-
criminative information, namely a sparse and invariant representation, from an image sequence that
is helpful for high-level tasks like object recognition. Un like these models, here we propose an
efficient inference procedure to extract locally invariant representation from image sequences and
progressively extract more abstract information at higher levels in the model.
Other methods used for building deep models, like restricted Boltzmann machine (RBM) [11], auto-
encoders [8, 12] and predictive sparse decomposition [13], are also related to the model proposed
here. All these models are constructed on similar underlyin g principles: (1) like ours, they also use
greedy layer-wise unsupervised learning to construct a hierarchical model and (2) each layer consists
of an encoder and a decoder. The key to these models is to learn both encoding and decoding
concurrently (with some regularization like sparsity [13] , denoising [8] or weight sharing [11]),
while building the deep network as a feed forward model using only the encoder. The idea is
to approximate the latent representation using only the fee d-forward encoder, while avoiding the
decoder which typically requires a more expensive inference procedure. However in DPCN there is
no encoder. Instead, DPCN relies on an efficient inference pr ocedure to get a more accurate latent
representation. As we will show below, the use of reciprocal top-down and bottom-up connections
make the proposed model more robust to structured noise duri ng recognition and also allows it to
perform low-level tasks like image denoising.
To scale to large images, several convolutional models are also proposed in a similar deep learning
paradigm [5–7]. Inference in these models is applied over anentire image, rather than small parts of
the input. DPCN can also be extended to form a convolutional network, but this will not be discussed
here.
2 Model
In this section, we begin with a brief description of the gene ral predictive coding framework and
proceed to discuss the details of the architecture used in this work. The basic block of the proposed
model that is pervasive across all layers is a generalized state-space model of the form:
˜ yt = F(xt) + nt
xt = G(xt−1, ut) + vt (1)
where ˜ yt is the data and F and G are some functions that can be parameterized, say byθ. The terms
ut are called the unknown causes . Since we are usually interested in obtaining abstract information
from the observations, the causes are encouraged to have a no n-linear relationship with the obser-
vations. The hidden states, xt, then “mediate the influence of the cause on the output and end ow
the system with memory” [10]. The terms vt and nt are stochastic and model uncertainty. Several
such state-space models can now be stacked, with the output from one acting as an input to the layer
above, to form a hierarchy. Such an L-layered hierarchical model at any time ’ t’ can be described
as1:
u(l−1 )
t = F(x(l)
t ) + n(l)
t ∀l ∈ { 1, 2, ..., L}
x(l)
t = G(x(l)
t−1, u(l)
t ) + v(l)
t (2)
The terms v(l)
t and n(l)
t form stochastic fluctuations at the higher layers and enter e ach layer in-
dependently. In other words, this model forms a Markov chain across the layers, simplifying the
inference procedure. Notice how the causes at the lower laye r form the “observations” to the layer
above — the causes form the link between the layers, and the st ates link the dynamics over time.
The important point in this design is that the higher-level p redictions influence the lower levels’
1When l = 1, i.e., at the bottom layer, u(i− 1)
t = yt, where yt the input data.
2
Causes (ut)
States (xt)
Observations (yt)
(a) Shows a single layered dynamic network
depicting a basic computational block.
- States (xt)
- Causes (ut)
(Invariant Units)
{ {Layer 1 Layer 2
(b) Shows the distributive hierarchical model formed by
stacking several basic blocks.
Figure 1: (a) Shows a single layered network on a group of smal l overlapping patches of the input
video. The green bubbles indicate a group of inputs ( y(n)
t , ∀n), red bubbles indicate their corre-
sponding states ( x(n)
t ) and the blue bubbles indicate the causes ( ut) that pool all the states within
the group. (b) Shows a two-layered hierarchical model const ructed by stacking several such basic
blocks. For visualization no overlapping is shown between the image patches here, but overlapping
patches are considered during actual implementation.
inference. The predictions from a higher layer non-linearl y enter into the state space model by em-
pirically altering the prior on the causes. In summary, the t op-down connections and the temporal
dependencies in the state space influence the latent representation at any layer.
In the following sections, we will first describe a basic comp utational network, as in (1) with a
particular form of the functions F and G. Specifically, we will consider a linear dynamical model
with sparse states for encoding the inputs and the state transitions, followed by the non-linear pooling
function to infer the causes. Next, we will discuss how to stack and learn a hierarchical model using
several of these basic networks. Also, we will discuss how to incorporate the top-down information
during inference in the hierarchical model.
2.1 Dynamic network
To begin with, we consider a dynamic network to extract featu res from a small part of a video
sequence. Let {y1, y2, ..., yt, ...} ∈ RP be a P -dimensional sequence of a patch extracted from
the same location across all the frames in a video 2 . To process this, our network consists of two
distinctive parts (see Figure.1a): feature extraction (inferring states) and pooling (inferring causes).
For the first part, sparse coding is used in conjunction with a linear state space model to map the
inputs yt at time t onto an over-complete dictionary of K-filters, C ∈ RP ×K (K > P ), to get
sparse states xt ∈ RK . To keep track of the dynamics in the latent states we use a lin ear function
with state-transition matrix A ∈ RK×K . More formally, inference of the features xt is performed
by finding a representation that minimizes the energy function:
E1(xt, yt, C, A) = ∥yt − Cxt∥2
2 + λ∥xt − Axt−1∥1 + γ ∥xt∥1 (3)
Notice that the second term involving the state-transition is also constrained to be sparse to make
the state-space representation consistent.
Now, to take advantage of the spatial relationships in a loca l neighborhood, a small group of states
x(n)
t , where n ∈ { 1, 2, ...N } represents a set of contiguous patches w.r.t. the position i n the image
space, are added (orsum pooled ) together. Such pooling of the states may be lead to local translation
invariance. On top this, a D-dimensional causes ut ∈ RD are inferred from the pooled states to
obtain representation that is invariant to more complex loc al transformations like rotation, spatial
frequency, etc. In line with [14], this invariant function i s learned such that it can capture the
dependencies between the components in the pooled states. S pecifically, the causes ut are inferred
2Here yt is a vectorized form of
√
P ×
√
P square patch extracted from a frame at time t.
3
by minimizing the energy function:
E2(ut, xt, B) =
N∑
n=1
( K∑
k=1
|γk · x(n)
t,k |
)
+ β∥ut∥1 (4)
γk = γ0
[ 1 + exp(−[But]k)
2
]
where γ0 > 0 is some constant. Notice that here ut multiplicatively interacts with the accumulated
states through B, modeling the shape of the sparse prior on the states. Essent ially, the invariant
matrix B is adapted such that each component ut connects to a group of components in the ac-
cumulated states that co-occur frequently. In other words, whenever a component in ut is active
it lowers the coefficient of a set of components in x(n)
t , ∀n, making them more likely to be active.
Since co-occurring components typically share some common statistical regularity, such activity of
ut typically leads to locally invariant representation [14].
Though the two cost functions are presented separately abov e, we can combine both to devise a
unified energy function of the form:
E(xt, ut, θ) =
N∑
n=1
(1
2∥y(n)
t − Cx(n)
t ∥2
2 + λ∥x(n)
t − Ax(n)
t−1∥1 +
K∑
k=1
|γt,k · x(n)
t,k |
)
+ β∥ut∥1
(5)
γt,k =γ0
[ 1 + exp(−[But]k)
2
]
where θ = {A, B, C}. As we will discuss next, both xt and ut can be inferred concurrently from
(5) by alternatively updating one while keeping the other fix ed using an efficient proximal gradient
method.
2.2 Learning
To learn the parameters in (5), we alternatively minimize E(xt, ut, θ) using a procedure similar to
block co-ordinate descent. We first infer the latent variabl es (xt, ut) while keeping the parameters
fixed and then update the parameters θ while keeping the variables fixed. This is done until the
parameters converge. We now discuss separately the inferen ce procedure and how we update the
parameters using a gradient descent method with the fixed variables.
2.2.1 Inference
We jointly infer bothxt and ut from (5) using proximal gradient methods, taking alternative gradient
descent steps to update one while holding the other fixed. In o ther words, we alternate between
updating xt and ut using a single update step to minimize E1 and E2, respectively. However,
updating xt is relatively more involved. So, keeping aside the causes, w e first focus on inferring
sparse states alone from E1, and then go back to discuss the joint inference of both the st ates and
the causes.
Inferring States: Inferring sparse states, given the parameters, from a linea r dynamical system
forms the crux of our model. This is performed by finding the so lution that minimizes the energy
function E1 in (3) with respect to the states xt (while keeping the sparsity parameter γ fixed).
Here there are two priors of the states: the temporal depende nce and the sparsity term. Although
this energy function E1 is convex in xt, the presence of two non-smooth terms makes it hard to
use standard optimization techniques used for sparse codin g alone. A similar problem is solved
using dynamic programming [15], homotopy [16] and Bayesian sparse coding [17]; however, the
optimization used in these models is computationally expensive for use in large scale problems like
object recognition.
To overcome this, inspired by the method proposed in [18] for structured sparsity, we propose an
approximate solution that is consistent and able to use effic ient solvers like fast iterative shrinkage
thresholding alogorithm (FISTA) [19]. The key to our approach is to first use Nestrov’s smoothness
method [18, 20] to approximate the non-smooth state transition term. The resulting energy function
4
is a convex and continuously differentiable function in xt with a sparsity constraint, and hence, can
be efficiently solved using proximal methods like FISTA.
To begin, letΩ( xt) = ∥et∥1 where et = ( xt − Axt−1). The idea is to find a smooth approximation
to this function Ω( xt) in et. Notice that, since et is a linear function on xt, the approximation will
also be smooth w.r.t. xt. Now, we can re-write Ω( xt) using the dual norm of ℓ1 as
Ω( xt) = arg max
∥α ∥∞ ≤1
α T et
where α ∈ Rk. Using the smoothing approximation from Nesterov [20] on Ω( xt):
Ω( xt) ≈ fµ (et) = arg max
∥α ∥∞ ≤1
[α T et − µd(α )] (6)
where d(·) = 1
2 ∥α ∥2
2 is a smoothing function and µ is a smoothness parameter. From Nestrov’s
theorem [20], it can be shown that fµ (et) is convex and continuously differentiable in et and the
gradient of fµ (et) with respect to et takes the form
∇et fµ (et) = α ∗ (7)
where α ∗ is the optimal solution to fµ (et) = arg max
∥α ∥∞ ≤1
[α T et − µd(α )] 3. This implies, by using
the chain rule, that fµ (et) is also convex and continuously differentiable in xt and with the same
gradient.
With this smoothing approximation, the overall cost function from (3) can now be re-written as
xt = arg min
xt
1
2∥yt − Cxt∥2
2 + λfµ (et) + γ∥xt∥1 (8)
with the smooth part h(xt) = 1
2 ∥yt − Cxt∥2
2 + λfµ (et) whose gradient with respect to xt is given
by
∇xt h(xt) = CT (yt − Cxt) + λα ∗ (9)
Using the gradient information in (9), we solve for xt from (8) using FISTA [19].
Inferring Causes: Given a group of state vectors, ut can be inferred by minimizing E2, where we
define a generative model that modulates the sparsity of thepooled state vector, ∑
n |x(n)|. Here we
observe that FISTA can be readily applied to infer ut, as the smooth part of the function E2:
h(ut) =
K∑
k=1
(
γ0
[ 1 + exp( −[But]k)
2
]
·
N∑
n=1
|x(n)
t,k |
)
(10)
is convex, continuously differentiable and Lipschitz inut [21] 4. Following [19], it is easy to obtain
a bound on the convergence rate of the solution.
Joint Inference: We showed thus far that bothxt and ut can be inferred from their respective energy
functions using a first-order proximal method called FISTA. However, for joint inference we have
to minimize the combined energy function in (5) over both xt and ut. We do this by alternately
updating xt and ut while holding the other fixed and using a single FISTA update step at each
iteration. It is important to point out that the internal FIS TA step size parameters are maintained
between iterations. This procedure is equivalent to alternating minimization using gradient descent.
Although this procedure no longer guarantees convergence of both xt and ut to the optimal solution,
in all of our simulations it lead to a reasonably good solutio n. Please refer to Algorithm. 1 (in the
supplementary material) for details. Note that, with the alternating update procedure, each xt is now
influenced by the feed-forward observations, temporal pred ictions and the feedback connections
from the causes.
3Please refer to the supplementary material for the exact form of α ∗.
4The matrix B is initialized with non-negative entries and continues to b e non-negative without any addi-
tional constraints [21].
5
2.2.2 Parameter Updates
With xt and ut fixed, we update the parameters by minimizing E in (5) with respect to θ. Since the
inputs here are a time-varying sequence, the parameters are updated using dual estimation filtering
[22]; i.e., we put an additional constraint on the parameter s such that they follow a state space
equation of the form:
θt = θt−1 + zt (11)
where zt is Gaussian transition noise over the parameters. This keep s track of their temporal rela-
tionships. Along with this constraint, we update the parame ters using gradient descent. Notice that
with a fixed xt and ut, each of the parameter matrices can be updated independentl y. Matrices C
and B are column normalized after the update to avoid any trivial solution.
Mini-Batch Update: To get faster convergence, the parameters are updated after performing infer-
ence over a large sequence of inputs instead of at every time instance. With this “batch” of signals,
more sophisticated gradient methods, like conjugate gradi ent, can be used and, hence, can lead to
more accurate and faster convergence.
2.3 Building a hierarchy
So far the discussion is focused on encoding a small part of a v ideo frame using a single stage
network. To build a hierarchical model, we use this single st age network as a basic building block
and arrange them up to form a tree structure (see Figure.1b). To learn this hierarchical mode l, we
adopt a greedy layer-wise procedure like many other deep learning methods [6, 8, 11]. Specifically,
we use the following strategy to learn the hierarchical model.
For the first (or bottom) layer, we learn a dynamic network as d escribed above over a group of
small patches from a video. We then take this learned network and replicate it at several places
on a larger part of the input frames (similar to weight sharin g in a convolutional network [23]).
The outputs (causes) from each of these replicated networks are considered as inputs to the layer
above. Similarly, in the second layer the inputs are again grouped together (depending on the spatial
proximity in the image space) and are used to train another dynamic network. Similar procedure can
be followed to build more higher layers.
We again emphasis that the model is learned in a layer-wise ma nner, i.e., there is no top-down
information while learning the network parameters. Also no te that, because of the pooling of the
states at each layers, the receptive field of the causes becomes progressively larger with the depth of
the model.
2.4 Inference with top-down information
With the parameters fixed, we now shift our focus to inference in the hierarchical model with the
top-down information. As we discussed above, the layers in the hierarchy are arranged in a Markov
chain, i.e., the variables at any layer are only influenced by the variables in the layer below and the
layer above. Specifically, the states x(l)
t and the causes u(l)
t at layer l are inferred from u(l−1)
t and
are influenced by x(l+1)
t (through the prediction term C(l+1)x(l+1)
t ) 5. Ideally, to perform inference
in this hierarchical model, all the states and the causes have to be updated simultaneously depending
on the present state of all the other layers until the model re aches equilibrium [10]. However, such
a procedure can be very slow in practice. Instead, we propose an approximate inference procedure
that only requires a single top-down flow of information and then a single bottom-up inference using
this top-down information.
5The suffixes n indicating the group are considered implicit here to simplify the notation.
6
For this we consider that at any layer l a group of input u(l−1,n )
t , ∀n ∈ { 1, 2, ..., N } are encoded
using a group of states x(l,n )
t , ∀n and the causes u(l)
t by minimizing the following energy function:
El(x(l)
t , u(l)
t , θ(l)) =
N∑
n=1
(1
2∥u(l−1,n )
t − C(l)x(l,n )
t ∥2
2 + λ∥x(l,n )
t − A(l)x(l,n )
t−1 ∥1
+
K∑
k=1
|γ(l)
t,k · x(l,n )
t,k |
)
+ β∥u(l)
t ∥1 + 1
2 ∥u(l)
t − ˆ u(l+1)
t ∥2
2 (12)
γ(l)
t,k = γ0
[ 1 + exp(−[B(l)u(l)
t ]k)
2
]
where θ(l) = {A(l), B(l), C(l)}. Notice the additional term involving ˆ u(l+1)
t when compared to (5).
This comes from the top-down information, where we call ˆ u(l+1)
t as the top-down prediction of the
causes of layer (l) using the previous states in layer (l + 1) . Specifically, before the “arrival” of a
new observation at time t, at each layer (l) (starting from the top-layer) we first propagate the most
likely causes to the layer below using the state at the previous time instance x(l)
t−1 and the predicted
causes ˆ u(l+1)
t . More formally, the top-down prediction at layer l is obtained as
ˆ u(l)
t = C(l)ˆ x(l)
t
where ˆ x(l)
t = arg min
x(l)
t
λ(l)∥x(l)
t − A(l)x(l)
t−1∥1 + γ0
K∑
k=1
|ˆγt,k · x(l)
t,k | (13)
and ˆγt,k = (exp( −[B(l)ˆ u(l+1)
t ]k))/2
At the top most layer, L, a “bias” is set such that ˆ u(L)
t = ˆ u(L)
t−1, i.e., the top-layer induces some
temporal coherence on the final outputs. From (13), it is easy to show that the predicted states for
layer l can be obtained as
ˆx(l)
t,k =
{
[A(l)x(l)
t−1]k, γ 0γt,k < λ (l)
0, γ 0γt,k ≥ λ(l) (14)
These predicted causesˆ u(l)
t , ∀l ∈ { 1, 2, ..., L} are substituted in (12) and a single layer-wise bottom-
up inference is performed as described in section 2.2.1 6. The combined prior now imposed on the
causes, β∥u(l)
t ∥1 + 1
2 ∥u(l)
t − ˆ u(l+1)
t ∥2
2, is similar to the elastic net prior discussed in [24], leading to
a smoother and biased estimate of the causes.
3 Experiments
3.1 Receptive fields of causes in the hierarchical model
Firstly, we would like to test the ability of the proposed mod el to learn complex features in the
higher-layers of the model. For this we train a two layered ne twork from a natural video. Each
frame in the video was first contrast normalized as described in [13]. Then, we train the first layer
of the model on 4 overlapping contiguous 15 × 15 pixel patches from this video; this layer has
400 dimensional states and 100 dimensional causes. The caus es pool the states related to all the
4 patches. The separation between the overlapping patches he re was 2 pixels, implying that the
receptive field of the causes in the first layer is 17 × 17 pixels. Similarly, the second layer is trained
on 4 causes from the first layer obtained from 4 overlapping 17 × 17 pixel patches from the video.
The separation between the patches here is 3 pixels, implying that the receptive field of the causes
in the second layer is 20 × 20 pixels. The second layer contains 200 dimensional states an d 50
dimensional causes that pools the states related to all the 4 patches.
Figure 2 shows the visualization of the receptive fields of th e invariant units (columns of matrix
B) at each layer. We observe that each dimension of causes in th e first layer represents a group of
6Note that the additional term 1
2 ∥u(l)
t − ˆ u(l+1)
t ∥2
2 in the energy function only leads to a minor modification
in the inference procedure, namely this has to be added to h(ut) in (10).
7
(a) Layer 1 invariant matrix, B(1)
(b) Layer 2 invariant matrix, B(2)
Figure 2: Visualization of the receptive fields of the invariant units learned in (a) layer 1 and (b) layer
2 when trained on natural videos. The receptive fields are constructed as a weighted combination of
the dictionary of filters at the bottom layer.
primitive features (like inclined lines) which are localized in orientation or position 7. Whereas, the
causes in the second layer represent more complex features, like corners, angles, etc. These filters
are consistent with the previously proposed methods like Lee et al. [5] and Zeiler et al. [7].
3.2 Role of top-down information
In this section, we show the role of the top-down information during inference, particularly in the
presence of structured noise. Video sequences consisting of objects of three different shapes (Refer
to Figure 3) were constructed. The objective is to classify e ach frame as coming from one of the
three different classes. For this, several 32 × 32 pixel 100 frame long sequences were made using
two objects of the same shape bouncing off each other and the “walls”. Several such sequences were
then concatenated to form a 30,000 long sequence. We train a two layer network using this sequence.
First, we divided each frame into12 × 12 patches with neighboring patches overlapping by 4 pixels;
each frame is divided into 16 patches. The bottom layer was tr ained such the 12 × 12 patches were
used as inputs and were encoded using a 100 dimensional state vector. A 4 contiguous neighboring
patches were pooled to infer the causes that have 40 dimensions. The second layer was trained with
4 first layer causes as inputs, which were itself inferred from20 × 20 contiguous overlapping blocks
of the video frames. The states here are 60 dimensional long and the causes have only 3 dimensions.
It is important to note here that the receptive field of the second layer causes encompasses the entire
frame.
We test the performance of the DPCN in two conditions. The firs t case is with 300 frames of clean
video, with 100 frames per shape, constructed as described above. We consider this as a single video
without considering any discontinuities. In the second case, we corrupt the clean video with “struc-
tured” noise, where we randomly pick a number of objects from same three shapes with a Poisson
distribution (with mean 1.5) and add them to each frame independently at a random locations. There
is no correlation between any two consecutive frames regarding where the “noisy objects” are added
(see Figure.3b).
First we consider the clean video and perform inference with only bottom-up inference, i.e., during
inference we consider ˆ u(l)
t = 0 , ∀l ∈ { 1, 2}. Figure 4a shows the scatter plot of the three dimen-
sional causes at the top layer. Clearly, there are 3 clusters recognizing three different shape in the
video sequence. Figure 4b shows the scatter plot when the sam e procedure is applied on the noisy
video. We observe that 3 shapes here can not be clearly distin guished. Finally, we use top-down
information along with the bottom-up inference as describe d in section 2.4 on the noisy data. We
argue that, since the second layer learned class specific inf ormation, the top-down information can
help the bottom layer units to disambiguate the noisy objects from the true objects. Figure 4c shows
the scatter plot for this case. Clearly, with the top-down in formation, in spite of largely corrupted
sequence, the DPCN is able to separate the frames belonging to the three shapes (the trace from one
cluster to the other is because of the temporal coherence imposed on the causes at the top layer.).
7Please refer to supplementary material for more results.
8
(a) Clear Sequences (b) Corrupted Sequences
Figure 3: Shows part of the (a) clean and (b) corrupted video s equences constructed using three
different shapes. Each row indicates one sequence.
0
5
10
0
2
4
0
2
4
6
Object 1
Object 2
Object 3
(a)
0
5
10
0
2
4
6
0
2
4
6
Object 1
Object 2
Object 3
(b)
0
2
4
6
0
1
2
3
0
2
4
6
Object 1
Object 2
Object 3
(c)
Figure 4: Shows the scatter plot of the 3 dimensional causes a t the top-layer for (a) clean video
with only bottom-up inference, (b) corrupted video with only bottom-up inference and (c) corrupted
video with top-down flow along with bottom-up inference. At e ach point, the shape of the marker
indicates the true shape of the object in the frame.
4 Conclusion
In this paper we proposed the deep predictive coding network , a generative model that empirically
alters the priors in a dynamic and context sensitive manner.This model composes to two main com-
ponents: (a) linear dynamical models with sparse states used for feature extraction, and (b) top-down
information to adapt the empirical priors. The dynamic mode l captures the temporal dependencies
and reduces the instability usually associated with sparse coding 8, while the task specific informa-
tion from the top layers helps to resolve ambiguities in the lower-layer improving data representation
in the presence of noise. We believe that our approach can be extended with convolutional methods,
paving the way for implementation of high-level tasks like o bject recognition, etc., on large scale
videos or images.
Acknowledgments
This work is supported by the Office of Naval Research (ONR) gr ant #N000141010375. We thank
Austin J. Brockmeier and Matthew Emigh for their comments and suggestions.
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10
A Supplementary material for Deep Predictive Coding Networ ks
A.1 From section 2.2.1, computing α ∗
The optimal solution of α in (6) is given by
α ∗ = arg max
∥α ∥∞ ≤1
[α T et − µ
2 ∥α ∥2]
= arg min
∥α ∥∞ ≤1
α − et
µ
2
=S
(et
µ
)
(15)
where S(.) is a function projecting
(
et
µ
)
onto an ℓ∞-ball. This is of the form:
S(x) =
x, −1 ≤ x ≤ 1
1, x > 1
−1, x < −1
A.2 Algorithm for joint inference of the states and the cause s.
Algorithm 1 Updating xt,ut simultaneously using FISTA-like procedure [19].
Require: Take Lx
0,n > 0 ∀n ∈ { 1, 2, ..., N }, Lu
0 > 0 and some η > 1.
1: Initialize x0,n ∈ RK ∀n ∈ { 1, 2, ..., N }, u0 ∈ RD and set ξ1 = u0, z1,n = x0,n .
2: Set step-size parameters: τ1 = 1 .
3: while no convergence do
4: Update
γ = γ0(1 + exp( −[Bui])/2
.
5: for n ∈ { 1, 2, ..., N } do
6: Line search: Find the best step size Lx
k,n .
7: Compute α ∗ from (15)
8: Update xi,n using the gradient from (9) with a soft-thresholding function.
9: Update internal variables zi+1 with step size parameter τi as in [19].
10: end for
11: Compute ∑ N
n=1 |xi,n |
12: Line search: Find the best step size Lu
k .
13: Update ui,n using the gradient of (10) with a soft-thresholding function.
14: Update internal variables ξi+1 with step size parameter τi as in [19].
15: Update
τi+1 =
(
1 +
√
(4τ2
i + 1)
)
/2
.
16: Check for convergence.
17: i = i + 1
18: end while
19: return xi,n ∀n ∈ { 1, 2, ..., N } and ui
11
A.3 Inferring sparse states with known parameters
20 40 60 80 1000
0.5
1
1.5
2
2.5
3
Observation Dimensions
steady state rMSE
Kalman Filter
Proposed
Sparse Coding [20]
Figure 5: Shows the performance of the inference algorithm w ith fixed parameters when compared
with sparse coding and Kalman filtering. For this we first simu late a state sequence with only 20
non-zero elements in a 500-dimensional state vector evolvi ng with a permutation matrix, which is
different for every time instant, followed by a scaling matrix to generate a sequence of observations.
We consider that both the permutation and the scaling matrices are known apriori. The observation
noise is Gaussian zero mean and variance σ2 = 0 .01. We consider sparse state-transition noise,
which is simulated by choosing a subset of active elements in the state vector (number of elements
is chosen randomly via a Poisson distribution with mean 2) an d switching each of them with a
randomly chosen element (with uniform probability over the state vector). This resemble a sparse
innovation in the states. We use these generated observation sequences as inputs and use the apriori
know parameters to infer the states from the dynamic model. F igure 5 shows the results obtained,
where we compare the inferred states from different methodswith the true states in terms of relative
mean squared error (rMSE) (defined as ∥xest
t − xtrue
t ∥/∥xtrue
t ∥). The steady state error (rMSE)
after 50 time instances is plotted versus with the dimension ality of the observation sequence. Each
point is obtained after averaging over 50 runs. We observe th at our model is able to converge to
the true solution even for low dimensional observation, when other methods like sparse coding fail.
We argue that the temporal dependencies considered in our model is able to drive the solution to the
right attractor basin, insulating it from instabilities typically associated with sparse coding [24].
12
A.4 Visualizing first layer of the learned model
(a) Observation matrix (Bases)
Active state
element at (t-1)
Corresponding,
predicted states at (t)
(b) State-transition matrix
Figure 6: Visualization of the parameters. C and A, of the model described in section 3.1. (A)
Shows the learned observation matrix C. Each square block indicates a column of the matrix,
reshaped as √p × √p pixel block. (B) Shows the state transition matrix A using its connections
strength with the observation matrix C. On the left are the basis corresponding to the single active
element in the state at time (t − 1) and on the right are the basis corresponding to the five most
“active” elements in the predicted state (ordered in decreasing order of the magnitude).
(a) Connections
(b) Centers and Orientations (c) Orientations and Frequencies
Figure 7: Connections between the invariant units and the ba sis functions. (A) Shows the connec-
tions between the basis and columns of B. Each row indicates an invariant unit. Here the set of
basis that a strongly correlated to an invariant unit are sho wn, arranged in the decreasing order of
the magnitude. (B) Shows spatially localized grouping of the invariant units. Firstly, we fit a Gabor
function to each of the basis functions. Each subplot here is then obtained by plotting a line indicat-
ing the center and the orientation of the Gabor function. Thecolors indicate the connections strength
with an invariant unit; red indicating stronger connection s and blue indicate almost zero strength.
We randomly select a subset of 25 invariant units here. We obs erve that the invariant unit group
the basis that are local in spatial centers and orientations . (C) Similarly, we show the correspond-
ing orientation and spatial frequency selectivity of the in variant units. Here each plot indicates the
orientation and frequency of each Gabor function color coded according to the connection strengths
with the invariant units. Each subplot is a half-polar plot with the orientation plotted along the angle
ranging from 0 to π and the distance from the center indicating the frequency. A gain, we observe
that the invariant units group the basis that have similar orientation.
13
|
Rakesh Chalasani, Jose C. Principe
|
Unknown
| 2,013
|
{"id": "yyC_7RZTkUD5-", "original": null, "cdate": null, "pdate": null, "odate": null, "mdate": null, "tcdate": 1358405100000, "tmdate": 1358405100000, "ddate": null, "number": 27, "content": {"title": "Deep Predictive Coding Networks", "decision": "conferencePoster-iclr2013-workshop", "abstract": "The quality of data representation in deep learning methods is directly related to the prior model imposed on the representations; however, generally used fixed priors are not capable of adjusting to the context in the data. To address this issue, we propose deep predictive coding networks, a hierarchical generative model that empirically alters priors on the latent representations in a dynamic and context-sensitive manner. This model captures the temporal dependencies in time-varying signals and uses top-down information to modulate the representation in lower layers. The centerpiece of our model is a novel procedure to infer sparse states of a dynamic model; which is used for feature extraction. We also extend this feature extraction block to introduce a pooling function that captures locally invariant representations. When applied on a natural video data, we show that our method is able to learn high-level visual features. We also demonstrate the role of the top-down connections by showing the robustness of the proposed model to structured noise.", "pdf": "https://arxiv.org/abs/1301.3541", "paperhash": "chalasani|deep_predictive_coding_networks", "authors": ["Rakesh Chalasani", "Jose C. Principe"], "authorids": ["vnit.rakesh@gmail.com", "principe@cnel.ufl.edu"], "keywords": [], "conflicts": []}, "forum": "yyC_7RZTkUD5-", "referent": null, "invitation": "ICLR.cc/2013/conference/-/submission", "replyto": null, "readers": ["everyone"], "nonreaders": [], "signatures": ["vnit.rakesh@gmail.com"], "writers": []}
|
[Review]:
Deep predictive coding networks
This paper introduces a new model which combines bottom-up, top-down, and temporal information to learning a generative model in an unsupervised fashion on videos. The model is formulated in terms of states, which carry temporal consistency information between time steps, and causes which are the latent variables inferred from the input image that attempt to explain what is in the image.
Pros:
Somewhat interesting filters are learned in the second layer of the model, though these have been shown in prior work.
Noise reduction on the toy images seems reasonable.
Cons:
The explanation of the model was overly complicated. After reading the the entire explanation it appears the model is simply doing sparse coding with ISTA alternating on the states and causes. The gradient for ISTA simply has the gradients for the overall cost function, just as in sparse coding but this cost function has some extra temporal terms.
The noise reduction is only on toy images and it is not obvious if this is what you would also get with sparse coding using larger patch sizes and high amounts of sparsity. The explanation of points between clusters coming from change in sequences should also appear in the clean video as well because as the text mentions the video changes as well. This is likely due to multiple objects overlapping instead and confusing the model.
Figure 1 should include the variable names because reading the text and consulting the figure is not very helpful currently.
It is hard to reason what each of the A,B, and C is doing without a picture of what they learn on typical data. The layer 1 features seem fairly complex and noisy for the first layer of an image model which typically learns gabor-like features.
Where did z come from in equation 11?
It is not at all obvious why the states should be temporally consistent and not the causes. The causes are pooled versions of the states and this should be more invariant to changes at the input between frames.
Novelty and Quality:
The paper introduces a novel extension to hierarchical sparse coding method by incorporating temporal information at each layer of the model. The poor explanation of this relatively simple idea holds the paper back slightly.
|
anonymous reviewer ac47
| null | null |
{"id": "d6u7vbCNJV6Q8", "original": null, "cdate": null, "pdate": null, "odate": null, "mdate": null, "tcdate": 1361968020000, "tmdate": 1361968020000, "ddate": null, "number": 3, "content": {"title": "review of Deep Predictive Coding Networks", "review": "Deep predictive coding networks\r\n\r\nThis paper introduces a new model which combines bottom-up, top-down, and temporal information to learning a generative model in an unsupervised fashion on videos. The model is formulated in terms of states, which carry temporal consistency information between time steps, and causes which are the latent variables inferred from the input image that attempt to explain what is in the image.\r\n\r\nPros:\r\nSomewhat interesting filters are learned in the second layer of the model, though these have been shown in prior work.\r\n\r\nNoise reduction on the toy images seems reasonable.\r\n\r\nCons:\r\nThe explanation of the model was overly complicated. After reading the the entire explanation it appears the model is simply doing sparse coding with ISTA alternating on the states and causes. The gradient for ISTA simply has the gradients for the overall cost function, just as in sparse coding but this cost function has some extra temporal terms.\r\n\r\nThe noise reduction is only on toy images and it is not obvious if this is what you would also get with sparse coding using larger patch sizes and high amounts of sparsity. The explanation of points between clusters coming from change in sequences should also appear in the clean video as well because as the text mentions the video changes as well. This is likely due to multiple objects overlapping instead and confusing the model.\r\n\r\nFigure 1 should include the variable names because reading the text and consulting the figure is not very helpful currently.\r\n\r\nIt is hard to reason what each of the A,B, and C is doing without a picture of what they learn on typical data. The layer 1 features seem fairly complex and noisy for the first layer of an image model which typically learns gabor-like features.\r\n\r\nWhere did z come from in equation 11?\r\n\r\nIt is not at all obvious why the states should be temporally consistent and not the causes. The causes are pooled versions of the states and this should be more invariant to changes at the input between frames.\r\n\r\nNovelty and Quality:\r\nThe paper introduces a novel extension to hierarchical sparse coding method by incorporating temporal information at each layer of the model. The poor explanation of this relatively simple idea holds the paper back slightly."}, "forum": "yyC_7RZTkUD5-", "referent": null, "invitation": "ICLR.cc/2013/-/submission/review", "replyto": "yyC_7RZTkUD5-", "readers": ["everyone"], "nonreaders": [], "signatures": ["anonymous reviewer ac47"], "writers": ["anonymous"]}
|
{
"criticism": 8,
"example": 0,
"importance_and_relevance": 2,
"materials_and_methods": 13,
"praise": 2,
"presentation_and_reporting": 3,
"results_and_discussion": 4,
"suggestion_and_solution": 3,
"total": 18
}
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| 0.111111
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{
"criticism": 0.4444444444444444,
"example": 0,
"importance_and_relevance": 0.1111111111111111,
"materials_and_methods": 0.7222222222222222,
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"results_and_discussion": 0.2222222222222222,
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