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Principal component analysis : Jackson, J.E. (1991). A User's Guide to Principal Components (Wiley). Jolliffe, I. T. (1986). Principal Component Analysis. Springer Series in Statistics. Springer-Verlag. pp. 487. CiteSeerX 10.1.1.149.8828. doi:10.1007/b98835. ISBN 978-0-387-95442-4. Jolliffe, I. T. (2002). Principal Com... |
Principal component analysis : University of Copenhagen video by Rasmus Bro on YouTube Stanford University video by Andrew Ng on YouTube A Tutorial on Principal Component Analysis A layman's introduction to principal component analysis on YouTube (a video of less than 100 seconds.) StatQuest: StatQuest: Principal Compo... |
Proper generalized decomposition : The proper generalized decomposition (PGD) is an iterative numerical method for solving boundary value problems (BVPs), that is, partial differential equations constrained by a set of boundary conditions, such as the Poisson's equation or the Laplace's equation. The PGD algorithm comp... |
Proper generalized decomposition : The proper generalized decomposition is a method characterized by a variational formulation of the problem, a discretization of the domain in the style of the finite element method, the assumption that the solution can be approximated as a separate representation and a numerical greed... |
Proper generalized decomposition : PGD is suitable for solving high-dimensional problems, since it overcomes the limitations of classical approaches. In particular, PGD avoids the curse of dimensionality, as solving decoupled problems is computationally much less expensive than solving multidimensional problems. Theref... |
Proper generalized decomposition : The Sparse Subspace Learning (SSL) method leverages the use of hierarchical collocation to approximate the numerical solution of parametric models. With respect to traditional projection-based reduced order modeling, the use of a collocation enables non-intrusive approach based on spa... |
Random indexing : Random indexing is a dimensionality reduction method and computational framework for distributional semantics, based on the insight that very-high-dimensional vector space model implementations are impractical, that models need not grow in dimensionality when new items (e.g. new terminology) are encou... |
Random indexing : Zadeh Behrang Qasemi, Handschuh Siegfried. (2015) Random indexing explained with high probability, TSD. |
Random projection : In mathematics and statistics, random projection is a technique used to reduce the dimensionality of a set of points which lie in Euclidean space. According to theoretical results, random projection preserves distances well, but empirical results are sparse. They have been applied to many natural la... |
Random projection : Dimensionality reduction, as the name suggests, is reducing the number of random variables using various mathematical methods from statistics and machine learning. Dimensionality reduction is often used to reduce the problem of managing and manipulating large data sets. Dimensionality reduction tech... |
Random projection : The core idea behind random projection is given in the Johnson-Lindenstrauss lemma, which states that if points in a vector space are of sufficiently high dimension, then they may be projected into a suitable lower-dimensional space in a way which approximately preserves pairwise distances between t... |
Random projection : The Johnson-Lindenstrauss lemma states that large sets of vectors in a high-dimensional space can be linearly mapped in a space of much lower (but still high) dimension n with approximate preservation of distances. One of the explanations of this effect is the exponentially high quasiorthogonal dime... |
Random projection : RandPro - An R package for random projection sklearn.random_projection - A module for random projection from the scikit-learn Python library Weka implementation [1] |
Random projection : Locality-sensitive hashing Random mapping Johnson-Lindenstrauss lemma |
Random projection : Fodor, Imola K (2002). A survey of dimension reduction techniques (Report). CiteSeerX 10.1.1.8.5098. Menon, Aditya Krishna (2007). Random projections and applications to dimensionality reduction (Thesis). CiteSeerX 10.1.1.164.640. Ramdas, Aditya. A Random Introduction To Random Projections (Report).... |
Relationship square : In statistics, the relationship square is a graphical representation for use in the factorial analysis of a table individuals x variables. This representation completes classical representations provided by principal component analysis (PCA) or multiple correspondence analysis (MCA), namely those ... |
Relationship square : The first interest of the relationship square is to represent the variables themselves, not their categories, which is all the more valuable as there are many variables. For this, we calculate for each qualitative variable j and each factor F s ( F s , rank s factor, is the vector of coordinat... |
Relationship square : Six individuals ( i 1 , … , i 6 ) ,\ldots ,i_) are described by three variables ( q 1 , q 2 , q 3 ) ,q_,q_) having respectively 3, 2 and 3 categories. Example : the individual i 1 possesses the category a of q 1 , d of q 2 and f of q 3 . Applied to these data, the MCA function included in t... |
Relationship square : This representation may be supplemented with those of quantitative variables, the coordinates of the latter being the square of correlation coefficients (and not of correlation ratios). Thus, the second advantage of the relationship square lies in the ability to represent simultaneously quantitati... |
Relationship square : The idea of representing the qualitative variables themselves by a point (and not the categories) is due to Brigitte Escofier. The graphic as it is used now has been introduced by Brigitte Escofier and Jérôme Pagès in the framework of multiple factor analysis |
Relationship square : In MCA, the relationship square provides a synthetic view of the connections between mixed variables, all the more valuable as there are many variables having many categories. This representation iscan be useful in any factorial analysis when there are numerous mixed variables, active and/or suppl... |
Relationship square : FactoMineR A R software devoted to exploratory data analysis. |
Relief (feature selection) : Relief is an algorithm developed by Kira and Rendell in 1992 that takes a filter-method approach to feature selection that is notably sensitive to feature interactions. It was originally designed for application to binary classification problems with discrete or numerical features. Relief c... |
Relief (feature selection) : Take a data set with n instances of p features, belonging to two known classes. Within the data set, each feature should be scaled to the interval [0 1] (binary data should remain as 0 and 1). The algorithm will be repeated m times. Start with a p-long weight vector (W) of zeros. At each it... |
Relief (feature selection) : Kononenko et al. propose a number of updates to Relief. Firstly, they find the near-hit and near-miss instances using the Manhattan (L1) norm rather than the Euclidean (L2) norm, although the rationale is not specified. Furthermore, they found taking the absolute differences between xi and ... |
Relief (feature selection) : The following RBAs are arranged chronologically from oldest to most recent. They include methods for improving (1) the core Relief algorithm concept, (2) iterative approaches for scalability, (3) adaptations to different data types, (4) strategies for computational efficiency, or (5) some c... |
Relief (feature selection) : Different RBAs have been applied to feature selection in a variety of problem domains. |
Relief (feature selection) : Feature Selection Nearest Neighbor Search == References == |
Robust principal component analysis : Robust Principal Component Analysis (RPCA) is a modification of the widely used statistical procedure of principal component analysis (PCA) which works well with respect to grossly corrupted observations. A number of different approaches exist for Robust PCA, including an idealized... |
Robust principal component analysis : RPCA has many real life important applications particularly when the data under study can naturally be modeled as a low-rank plus a sparse contribution. Following examples are inspired by contemporary challenges in computer science, and depending on the applications, either the low... |
Robust principal component analysis : L1-norm principal component analysis |
Robust principal component analysis : Robust PCA Dynamic RPCA Decomposition into Low-rank plus Additive Matrices Low-rank models |
Semantic mapping (statistics) : Semantic mapping (SM) is a statistical method for dimensionality reduction (the transformation of data from a high-dimensional space into a low-dimensional space). SM can be used in a set of multidimensional vectors of features to extract a few new features that preserves the main data c... |
Semantic mapping (statistics) : Dimensionality reduction Principal components analysis Latent semantic indexing Unification (logic reduction) |
Semantic mapping (statistics) : CORRÊA, R. F.; LUDERMIR, T. B. Improving Self Organization of Document Collections by Semantic Mapping. Neurocomputing(Amsterdam), v. 70, p. 62-69, 2006. doi:10.1016/j.neucom.2006.07.007 CORRÊA, R. F. and LUDERMIR, T. B. (2007) "Dimensionality Reduction of very large document collections... |
Semantic mapping (statistics) : Full list of publications about Semantic Mapping method |
Semidefinite embedding : Maximum Variance Unfolding (MVU), also known as Semidefinite Embedding (SDE), is an algorithm in computer science that uses semidefinite programming to perform non-linear dimensionality reduction of high-dimensional vectorial input data. It is motivated by the observation that kernel Principal ... |
Semidefinite embedding : MVU creates a mapping from the high dimensional input vectors to some low dimensional Euclidean vector space in the following steps: A neighbourhood graph is created. Each input is connected with its k-nearest input vectors (according to Euclidean distance metric) and all k-nearest neighbors ar... |
Semidefinite embedding : Let X be the original input and Y be the embedding. If i , j are two neighbors, then the local isometry constraint that needs to be satisfied is: | X i − X j | 2 = | Y i − Y j | 2 -X_|^=|Y_-Y_|^\,\! Let G , K be the Gram matrices of X and Y (i.e.: G i j = X i ⋅ X j , K i j = Y i ⋅ Y j =X_... |
Semidefinite embedding : Locally linear embedding Isometry (disambiguation) Local Tangent Space Alignment Riemannian manifold Energy minimization |
Semidefinite embedding : Linial, London and Rabinovich, Nathan, Eran and Yuri (1995). "The geometry of graphs and some of its algorithmic applications". Combinatorica. 15 (2): 215–245. doi:10.1007/BF01200757. S2CID 5071936.: CS1 maint: multiple names: authors list (link) Weinberger, Sha and Saul, Kilian Q., Fei and Law... |
Semidefinite embedding : Kilian Q. Weinberger's MVU Matlab code |
Sliced inverse regression : Sliced inverse regression (SIR) is a tool for dimensionality reduction in the field of multivariate statistics. In statistics, regression analysis is a method of studying the relationship between a response variable y and its input variable x _ , which is a p-dimensional vector. There are s... |
Sliced inverse regression : Given a response variable Y and a (random) vector X ∈ R p ^ of explanatory variables, SIR is based on the model Y = f ( β 1 ⊤ X , … , β k ⊤ X , ε ) ( 1 ) ^X,\ldots ,\beta _^X,\varepsilon )\quad \quad \quad \quad \quad (1) where β 1 , … , β k ,\ldots ,\beta _ are unknown projection vectors,... |
Sliced inverse regression : Given a _ 1 , … , a _ r ∈ R n _,\ldots ,_\in \mathbb ^ , then V := L ( a _ 1 , … , a _ r ) _,\ldots ,_) , the set of all linear combinations of these vectors is called a linear subspace and is therefore a vector space. The equation says that vectors a _ 1 , … , a _ r _,\ldots ,_ span V , b... |
Sliced inverse regression : Computing the inverse regression curve (IR) means instead of looking for E [ Y | X = x ] , which is a curve in R p ^ it is actually E [ X | Y = y ] , which is also a curve in R p ^ , but consisting of p one-dimensional regressions. The center of the inverse regression curve is located a... |
Sliced inverse regression : The centered inverse regression curve lies on a k -dimensional subspace spanned by Σ x x β i ′ s \beta _\,'s . This is a connection between the model and inverse regression. Given this condition and ( 1 ) , the centered inverse regression curve E [ X | Y = y ] − E [ X ] is contained in th... |
Sliced inverse regression : After having had a look at all the theoretical properties, the aim now is to estimate the EDR-directions. For that purpose, weighted principal component analyses are needed. If the sample means m ^ h ′ s _\,'s , X would have been standardized to Z = Σ x x − 1 / 2 ^\ . Corresponding to the ... |
Sliced inverse regression : Li, K-C. (1991) "Sliced Inverse Regression for Dimension Reduction", Journal of the American Statistical Association, 86, 316–327 Jstor Cook, R.D. and Sanford Weisberg, S. (1991) "Sliced Inverse Regression for Dimension Reduction: Comment", Journal of the American Statistical Association, 86... |
Stress majorization : Stress majorization is an optimization strategy used in multidimensional scaling (MDS) where, for a set of n m -dimensional data items, a configuration X of n points in r ( ≪ m ) -dimensional space is sought that minimizes the so-called stress function σ ( X ) . Usually r is 2 or 3 , i.e... |
Stress majorization : The stress function σ can be expanded as follows: σ ( X ) = ∑ i < j ≤ n w i j ( d i j ( X ) − δ i j ) 2 = ∑ i < j w i j δ i j 2 + ∑ i < j w i j d i j 2 ( X ) − 2 ∑ i < j w i j δ i j d i j ( X ) w_(d_(X)-\delta _)^=\sum _w_\delta _^+\sum _w_d_^(X)-2\sum _w_\delta _d_(X) Note that the first term is... |
Stress majorization : Stress majorization and algorithms similar to SMACOF also have application in the field of graph drawing. That is, one can find a reasonably aesthetically appealing layout for a network or graph by minimizing a stress function over the positions of the nodes in the graph. In this case, the δ i j ... |
Sufficient dimension reduction : In statistics, sufficient dimension reduction (SDR) is a paradigm for analyzing data that combines the ideas of dimension reduction with the concept of sufficiency. Dimension reduction has long been a primary goal of regression analysis. Given a response variable y and a p-dimensional p... |
Sufficient dimension reduction : In a regression setting, it is often useful to summarize the distribution of y ∣ x graphically. For instance, one may consider a scatterplot of y versus one or more of the predictors or a linear combination of the predictors. A scatterplot that contains all available regression inform... |
Sufficient dimension reduction : Suppose R ( x ) = A T x )=A^ is a sufficient dimension reduction, where A is a p × k matrix with rank k ≤ p . Then the regression information for y ∣ x can be inferred by studying the distribution of y ∣ A T x , and the plot of y versus A T x is a sufficient summary plot. Without... |
Sufficient dimension reduction : If a subspace S is a DRS for y ∣ x , and if S ⊂ S drs \subset _ for all other DRSs S drs _ , then it is a central dimension reduction subspace, or simply a central subspace, and it is denoted by S y ∣ x _ . In other words, a central subspace for y ∣ x exists if and only if the inters... |
Sufficient dimension reduction : There are many existing methods for dimension reduction, both graphical and numeric. For example, sliced inverse regression (SIR) and sliced average variance estimation (SAVE) were introduced in the 1990s and continue to be widely used. Although SIR was originally designed to estimate a... |
Sufficient dimension reduction : Dimension reduction Sliced inverse regression Principal component analysis Linear discriminant analysis Curse of dimensionality Multilinear subspace learning |
Tensor sketch : In statistics, machine learning and algorithms, a tensor sketch is a type of dimensionality reduction that is particularly efficient when applied to vectors that have tensor structure. Such a sketch can be used to speed up explicit kernel methods, bilinear pooling in neural networks and is a cornerstone... |
Tensor sketch : Mathematically, a dimensionality reduction or sketching matrix is a matrix M ∈ R k × d ^ , where k < d , such that for any vector x ∈ R d ^ | ‖ M x ‖ 2 − ‖ x ‖ 2 | < ε ‖ x ‖ 2 -\|x\|_|<\varepsilon \|x\|_ with high probability. In other words, M preserves the norm of vectors up to a small error. A te... |
Tensor sketch : The term tensor sketch was coined in 2013 describing a technique by Rasmus Pagh from the same year. Originally it was understood using the fast Fourier transform to do fast convolution of count sketches. Later research works generalized it to a much larger class of dimensionality reductions via Tensor r... |
Tensor sketch : The face-splitting product is defined as the tensor products of the rows (was proposed by V. Slyusar in 1996 for radar and digital antenna array applications). More directly, let C ∈ R 3 × 3 \in \mathbb ^ and D ∈ R 3 × 3 \in \mathbb ^ be two matrices. Then the face-splitting product C ∙ D \bullet \... |
Tensor sketch : It is also possible to do so-called "data aware" tensor sketching. Instead of multiplying a random matrix on the data, the data points are sampled independently with a certain probability depending on the norm of the point. |
Tensor sketch : Ahle, Thomas; Knudsen, Jakob (2019-09-03). "Almost Optimal Tensor Sketch". ResearchGate. Retrieved 2020-07-11. Slyusar, V. I. (1998). "End products in matrices in radar applications" (PDF). Radioelectronics and Communications Systems. 41 (3): 50–53. Slyusar, V. I. (1997-05-20). "Analytical model of the ... |
List of datasets for machine-learning research : These datasets are used in machine learning (ML) research and have been cited in peer-reviewed academic journals. Datasets are an integral part of the field of machine learning. Major advances in this field can result from advances in learning algorithms (such as deep le... |
List of datasets for machine-learning research : The data portal is classified based on its type of license. The open source license based data portals are known as open data portals which are used by many government organizations and academic institutions. |
List of datasets for machine-learning research : The data portal sometimes lists a wide variety of subtypes of datasets pertaining to many machine learning applications. |
List of datasets for machine-learning research : The data portals which are suitable for a specific subtype of machine learning application are listed in the subsequent sections. |
List of datasets for machine-learning research : These datasets consist primarily of text for tasks such as natural language processing, sentiment analysis, translation, and cluster analysis. |
List of datasets for machine-learning research : These datasets consist of sounds and sound features used for tasks such as speech recognition and speech synthesis. |
List of datasets for machine-learning research : Datasets containing electric signal information requiring some sort of signal processing for further analysis. |
List of datasets for machine-learning research : This section includes datasets that deals with structured data. |
List of datasets for machine-learning research : As datasets come in myriad formats and can sometimes be difficult to use, there has been considerable work put into curating and standardizing the format of datasets to make them easier to use for machine learning research. OpenML: Web platform with Python, R, Java, and ... |
List of datasets for machine-learning research : Comparison of deep learning software List of manual image annotation tools List of biological databases == References == |
Arabic Speech Corpus : The Arabic Speech Corpus is a Modern Standard Arabic (MSA) speech corpus for speech synthesis. The corpus contains phonetic and orthographic transcriptions of more than 3.7 hours of MSA speech aligned with recorded speech on the phoneme level. The annotations include word stress marks on the indi... |
Arabic Speech Corpus : The corpus was mainly built for speech synthesis purposes, specifically Speech Synthesis, but the corpus has been used for building HMM based voices in Arabic. It was also used to automatically align other speech corpora with their phonetic transcript and could be used as part of a larger corpus ... |
Arabic Speech Corpus : The package contains the following: 1813 .wav files containing spoken utterances. 1813 .lab files containing text utterances. 1813 .TextGrid files containing the phoneme labels with time stamps of the boundaries where these occur in the .wav files. phonetic-transcript.txt which has the form "[wav... |
Arabic Speech Corpus : Comparison of datasets in machine learning |
Arabic Speech Corpus : The Arabic Speech Corpus official website The Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License |
BookCorpus : BookCorpus (also sometimes referred to as the Toronto Book Corpus) is a dataset consisting of the text of around 7,000 self-published books scraped from the indie ebook distribution website Smashwords. It was the main corpus used to train the initial GPT model by OpenAI, and has been used as training data ... |
Common Voice : Common Voice is a crowdsourcing project started by Mozilla to create a free database for speech recognition software. The project is supported by volunteers who record sample sentences with a microphone and review recordings of other users. The transcribed sentences are collected in a voice database avai... |
Common Voice : Common Voice aims to provide diverse voice samples. According to Mozilla's Katharina Borchert, many existing projects took datasets from public radio or otherwise had datasets that underrepresented both women and people with pronounced accents. |
Common Voice : At the beginning of 2022, Bengali.AI partnered with Common Voice to launch "Bangla Speech Recognition" project that aims to make machines understand Bangla language. 2000 hours of voice was collected with aim for higher than 10,000 hours. |
Common Voice : The first dataset was released in November 2017. More than 20,000 users worldwide had recorded 500 hours of English sentences. In February 2019, the first batch of languages was released for use. This included 18 languages: English, French, German and Mandarin Chinese, but also less prevalent languages a... |
Common Voice : Forvo Lingua Libre Crowdsource (app) == References == |
Iris flower data set : The Iris flower data set or Fisher's Iris data set is a multivariate data set used and made famous by the British statistician and biologist Ronald Fisher in his 1936 paper The use of multiple measurements in taxonomic problems as an example of linear discriminant analysis. It is sometimes called... |
Iris flower data set : Originally used as an example data set on which Fisher's linear discriminant analysis was applied, it became a typical test case for many statistical classification techniques in machine learning such as support vector machines. The use of this data set in cluster analysis however is not common, ... |
Iris flower data set : The dataset contains a set of 150 records under five attributes: sepal length, sepal width, petal length, petal width and species. The iris data set is widely used as a beginner's dataset for machine learning purposes. The dataset is included in R base and Python in the machine learning library s... |
Iris flower data set : Classic data sets List of datasets for machine-learning research |
Iris flower data set : "Fisher's Iris Data". (Contains two errors which are documented). UCI Machine Learning Repository: Iris Data Set. |
LamaH : LamaH (Large-Sample Data for Hydrology and Environmental Sciences) is a cross-state initiative for unified data preparation and collection in the field of catchment hydrology. Hydrological datasets, for example, are an integral component for creating flood forecasting models. |
LamaH : LamaH datasets always consist of a combination of meteorological time series (e.g., precipitation, temperature) and hydrologically relevant catchment attributes (e.g., elevation, slope, forest area, soil, bedrock) aggregated over the respective catchment as well as associated hydrological time series at the cat... |
LamaH : The LamaH datasets are quite similar to the CAMELS datasets, but additionally feature: Further basin delineations (based on intermediate catchments) and attributes (e.g. flow distance and altitude difference between two topologically adjacent discharge gauges), enabling the setup of a interconnected hydrologica... |
LamaH : LamaH datasets are available for the following regions: Central Europe (Austria and its hydrological upstream areas in Germany, Czech Republic, Switzerland, Slovakia, Italy, Liechtenstein, Slovenia and Hungary) / 859 catchments CAMELS datasets are available for (ranked by publication date): Contiguous USA (excl... |
Language model benchmark : Language model benchmarks are standardized tests designed to evaluate the performance of language models on various natural language processing tasks. These tests are intended for comparing different models' capabilities in areas such as language understanding, generation, and reasoning. Benc... |
Language model benchmark : List of large language models List of datasets for machine-learning research |
Language model benchmark : Epoch AI - AI Benchmarking Hub == References == |
PCVC Speech Dataset : The PCVC (Persian Consonant Vowel Combination) Speech Dataset is a Modern Persian speech corpus for speech recognition and also speaker recognition. The dataset contains sound samples of Modern Persian combination of vowel and consonant phonemes from different speakers. Every sound sample contains... |
PCVC Speech Dataset : The corpus is downloadable from its Kaggle web page, and contains the following: .mat data files of sound samples in a 23*6*30000 matrix, in which 23 is number of consonants, 6 is the number of vowels and 30000 is the length of sound sample. |
PCVC Speech Dataset : Comparison of datasets in machine learning |
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