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Evolutionary multimodal optimization : De Jong's crowding method, Goldberg's sharing function approach, Petrowski's clearing method, restricted mating, maintaining multiple subpopulations are some of the popular approaches that have been proposed by the community. The first two methods are especially well studied, howe... |
Evolutionary multimodal optimization : Multi-modal optimization using Particle Swarm Optimization (PSO) Niching in Evolution Strategies (ES) Multimodal optimization page at Chair 11, Computer Science, TU Dortmund University IEEE CIS Task Force on Multi-modal Optimization |
Expectation–maximization algorithm : In statistics, an expectation–maximization (EM) algorithm is an iterative method to find (local) maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. The EM iteration alternates betwee... |
Expectation–maximization algorithm : The EM algorithm was explained and given its name in a classic 1977 paper by Arthur Dempster, Nan Laird, and Donald Rubin. They pointed out that the method had been "proposed many times in special circumstances" by earlier authors. One of the earliest is the gene-counting method for... |
Expectation–maximization algorithm : The EM algorithm is used to find (local) maximum likelihood parameters of a statistical model in cases where the equations cannot be solved directly. Typically these models involve latent variables in addition to unknown parameters and known data observations. That is, either missin... |
Expectation–maximization algorithm : Although an EM iteration does increase the observed data (i.e., marginal) likelihood function, no guarantee exists that the sequence converges to a maximum likelihood estimator. For multimodal distributions, this means that an EM algorithm may converge to a local maximum of the obse... |
Expectation–maximization algorithm : Expectation-Maximization works to improve Q ( θ ∣ θ ( t ) ) \mid ^) rather than directly improving log p ( X ∣ θ ) \mid ) . Here it is shown that improvements to the former imply improvements to the latter. For any Z with non-zero probability p ( Z ∣ X , θ ) \mid \mathbf ,) ,... |
Expectation–maximization algorithm : The EM algorithm can be viewed as two alternating maximization steps, that is, as an example of coordinate descent. Consider the function: F ( q , θ ) := E q [ log L ( θ ; x , Z ) ] + H ( q ) , _[\log L(\theta ;x,Z)]+H(q), where q is an arbitrary probability distribution over t... |
Expectation–maximization algorithm : EM is frequently used for parameter estimation of mixed models, notably in quantitative genetics. In psychometrics, EM is an important tool for estimating item parameters and latent abilities of item response theory models. With the ability to deal with missing data and observe unid... |
Expectation–maximization algorithm : A Kalman filter is typically used for on-line state estimation and a minimum-variance smoother may be employed for off-line or batch state estimation. However, these minimum-variance solutions require estimates of the state-space model parameters. EM algorithms can be used for solvi... |
Expectation–maximization algorithm : A number of methods have been proposed to accelerate the sometimes slow convergence of the EM algorithm, such as those using conjugate gradient and modified Newton's methods (Newton–Raphson). Also, EM can be used with constrained estimation methods. Parameter-expanded expectation ma... |
Expectation–maximization algorithm : EM is a partially non-Bayesian, maximum likelihood method. Its final result gives a probability distribution over the latent variables (in the Bayesian style) together with a point estimate for θ (either a maximum likelihood estimate or a posterior mode). A fully Bayesian version of... |
Expectation–maximization algorithm : In information geometry, the E step and the M step are interpreted as projections under dual affine connections, called the e-connection and the m-connection; the Kullback–Leibler divergence can also be understood in these terms. |
Expectation–maximization algorithm : EM typically converges to a local optimum, not necessarily the global optimum, with no bound on the convergence rate in general. It is possible that it can be arbitrarily poor in high dimensions and there can be an exponential number of local optima. Hence, a need exists for alterna... |
Expectation–maximization algorithm : mixture distribution compound distribution density estimation Principal component analysis total absorption spectroscopy The EM algorithm can be viewed as a special case of the majorize-minimization (MM) algorithm. |
Expectation–maximization algorithm : Hogg, Robert; McKean, Joseph; Craig, Allen (2005). Introduction to Mathematical Statistics. Upper Saddle River, NJ: Pearson Prentice Hall. pp. 359–364. Dellaert, Frank (February 2002). The Expectation Maximization Algorithm (PDF) (Technical Report number GIT-GVU-02-20). Georgia Tech... |
Expectation–maximization algorithm : Various 1D, 2D and 3D demonstrations of EM together with Mixture Modeling are provided as part of the paired SOCR activities and applets. These applets and activities show empirically the properties of the EM algorithm for parameter estimation in diverse settings. Class hierarchy in... |
FastICA : FastICA is an efficient and popular algorithm for independent component analysis invented by Aapo Hyvärinen at Helsinki University of Technology. Like most ICA algorithms, FastICA seeks an orthogonal rotation of prewhitened data, through a fixed-point iteration scheme, that maximizes a measure of non-Gaussian... |
FastICA : Unsupervised learning Machine learning The IT++ library features a FastICA implementation in C++ Infomax |
FastICA : FastICA in Python FastICA package for Matlab or Octave fastICA package in R programming language FastICA in Java on SourceForge FastICA in Java in RapidMiner. FastICA in Matlab FastICA in MDP FastICA in Julia |
Federated Learning of Cohorts : Federated Learning of Cohorts (FLoC) is a type of web tracking. It groups people into "cohorts" based on their browsing history for the purpose of interest-based advertising. FLoC was being developed as a part of Google's Privacy Sandbox initiative, which includes several other advertisi... |
Federated Learning of Cohorts : The Federated Learning of Cohorts algorithm analyzes users' online activity within the browser, and generates a "cohort ID" using the SimHash algorithm to group a given user with other users who access similar content.: 9 Each cohort contains several thousand users in order to make ident... |
Federated Learning of Cohorts : Google claimed in January 2021 that FLoC was at least 95% effective compared to tracking using third-party cookies, but AdExchanger reported that some people in the advertising technology industry expressed skepticism about the claim and the methodology behind it. As every website that o... |
Federated Learning of Cohorts : Am I FLoCed?—EFF website reporting to users if FLoC is enabled FLoCs explained at the Privacy Sandbox Initiative website More detailed FLoC Origin Trial & Clustering – infos from the Chromium project |
Gaussian splatting : Gaussian splatting is a volume rendering technique that deals with the direct rendering of volume data without converting the data into surface or line primitives. The technique was originally introduced as splatting by Lee Westover in the early 1990s. With advancements in computer graphics, newer ... |
Gaussian splatting : 3D Gaussian splatting is a technique used in the field of real-time radiance field rendering. It enables the creation of high-quality real-time novel-view scenes by combining multiple photos or videos, addressing a significant challenge in the field. The method represents scenes with 3D Gaussians t... |
Gaussian splatting : Extending 3D Gaussian splatting to dynamic scenes, 3D Temporal Gaussian splatting incorporates a time component, allowing for real-time rendering of dynamic scenes with high resolutions. It represents and renders dynamic scenes by modeling complex motions while maintaining efficiency. The method us... |
Gaussian splatting : 3D Gaussian splatting has been adapted and extended across various computer vision and graphics applications, from dynamic scene rendering to autonomous driving simulations and 4D content creation: Text-to-3D using Gaussian Splatting: Applies 3D Gaussian splatting to text-to-3D generation. End-to-e... |
Gaussian splatting : Computer graphics Neural radiance field Volume rendering == References == |
GeneRec : GeneRec is a generalization of the recirculation algorithm, and approximates Almeida-Pineda recurrent backpropagation. It is used as part of the Leabra algorithm for error-driven learning. The symmetric, midpoint version of GeneRec is equivalent to the contrastive Hebbian learning algorithm (CHL). |
GeneRec : Leabra O'Reilly (1996; Neural Computation) == References == |
Genetic Algorithm for Rule Set Production : Genetic Algorithm for Rule Set Production (GARP) is a computer program based on genetic algorithm that creates ecological niche models for species. The generated models describe environmental conditions (precipitation, temperatures, elevation, etc.) under which the species sh... |
Genetic Algorithm for Rule Set Production : Stockwell, D. R. B. 1999. Genetic algorithms II. Pages 123–144 in A. H. Fielding, editor. Machine learning methods for ecological applications. Kluwer Academic Publishers, Boston Stockwell, D. R. B., and D. G. Peters. 1999. The GARP modelling system: Problems and solutions to... |
Genetic Algorithm for Rule Set Production : OpenModeller – (related GARP page) Lifemapper |
Graphical time warping : Graphical time warping (GTW) is a framework for jointly aligning multiple pairs of time series or sequences. GTW considers both the alignment accuracy of each sequence pair and the similarity among pairs. On contrary, alignment with dynamic time warping (DTW) considers the pairs independently a... |
Graphical time warping : Dynamic time warping Elastic matching Sequence alignment Multiple sequence alignment == References == |
IDistance : In pattern recognition, iDistance is an indexing and query processing technique for k-nearest neighbor queries on point data in multi-dimensional metric spaces. The kNN query is one of the hardest problems on multi-dimensional data, especially when the dimensionality of the data is high. iDistance is design... |
IDistance : Building the iDistance index has two steps: A number of reference points in the data space are chosen. There are various ways of choosing reference points. Using cluster centers as reference points is the most efficient way. The data points are partitioned into Voronoi cells based on well-chosen reference p... |
IDistance : To process a kNN query, the query is mapped to a number of one-dimensional range queries, which can be processed efficiently on a B+-tree. In the above figure, the query Q is mapped to a value in the B+-tree while the kNN search ``sphere" is mapped to a range in the B+-tree. The search sphere expands gradua... |
IDistance : The iDistance has been used in many applications including Image retrieval Video indexing Similarity search in P2P systems Mobile computing Recommender system |
IDistance : The iDistance was first proposed by Cui Yu, Beng Chin Ooi, Kian-Lee Tan and H. V. Jagadish in 2001. Later, together with Rui Zhang, they improved the technique and performed a more comprehensive study on it in 2005. |
IDistance : Filter and refine |
IDistance : iDistance implementation in C by Rui Zhang Google's iDistance implementation in C++ Early Separation of Filter and Refinement Steps in Spatial Query Optimization Filter and Refine Principle (FRP) |
Incremental learning : In computer science, incremental learning is a method of machine learning in which input data is continuously used to extend the existing model's knowledge i.e. to further train the model. It represents a dynamic technique of supervised learning and unsupervised learning that can be applied when ... |
Incremental learning : Transduction (machine learning) |
Incremental learning : charleslparker (March 12, 2013). "Brief Introduction to Streaming data and Incremental Algorithms". BigML Blog. Gepperth, Alexander; Hammer, Barbara (2016). Incremental learning algorithms and applications (PDF). ESANN. pp. 357–368. LibTopoART: A software library for incremental learning tasks "C... |
K-nearest neighbors algorithm : In statistics, the k-nearest neighbors algorithm (k-NN) is a non-parametric supervised learning method. It was first developed by Evelyn Fix and Joseph Hodges in 1951, and later expanded by Thomas Cover. Most often, it is used for classification, as a k-NN classifier, the output of which... |
K-nearest neighbors algorithm : Suppose we have pairs ( X 1 , Y 1 ) , ( X 2 , Y 2 ) , … , ( X n , Y n ) ,Y_),(X_,Y_),\dots ,(X_,Y_) taking values in R d × ^\times \ , where Y is the class label of X, so that X | Y = r ∼ P r for r = 1 , 2 (and probability distributions P r ). Given some norm ‖ ⋅ ‖ on R d ^ and a ... |
K-nearest neighbors algorithm : The training examples are vectors in a multidimensional feature space, each with a class label. The training phase of the algorithm consists only of storing the feature vectors and class labels of the training samples. In the classification phase, k is a user-defined constant, and an unl... |
K-nearest neighbors algorithm : The best choice of k depends upon the data; generally, larger values of k reduces effect of the noise on the classification, but make boundaries between classes less distinct. A good k can be selected by various heuristic techniques (see hyperparameter optimization). The special case whe... |
K-nearest neighbors algorithm : The most intuitive nearest neighbour type classifier is the one nearest neighbour classifier that assigns a point x to the class of its closest neighbour in the feature space, that is C n 1 n n ( x ) = Y ( 1 ) ^(x)=Y_ . As the size of training data set approaches infinity, the one neares... |
K-nearest neighbors algorithm : The k-nearest neighbour classifier can be viewed as assigning the k nearest neighbours a weight 1 / k and all others 0 weight. This can be generalised to weighted nearest neighbour classifiers. That is, where the ith nearest neighbour is assigned a weight w n i , with ∑ i = 1 n w n i =... |
K-nearest neighbors algorithm : k-NN is a special case of a variable-bandwidth, kernel density "balloon" estimator with a uniform kernel. The naive version of the algorithm is easy to implement by computing the distances from the test example to all stored examples, but it is computationally intensive for large trainin... |
K-nearest neighbors algorithm : There are many results on the error rate of the k nearest neighbour classifiers. The k-nearest neighbour classifier is strongly (that is for any joint distribution on ( X , Y ) ) consistent provided k := k n diverges and k n / n /n converges to zero as n → ∞ . Let C n k n n ^ denote t... |
K-nearest neighbors algorithm : The K-nearest neighbor classification performance can often be significantly improved through (supervised) metric learning. Popular algorithms are neighbourhood components analysis and large margin nearest neighbor. Supervised metric learning algorithms use the label information to learn... |
K-nearest neighbors algorithm : When the input data to an algorithm is too large to be processed and it is suspected to be redundant (e.g. the same measurement in both feet and meters) then the input data will be transformed into a reduced representation set of features (also named features vector). Transforming the in... |
K-nearest neighbors algorithm : For high-dimensional data (e.g., with number of dimensions more than 10) dimension reduction is usually performed prior to applying the k-NN algorithm in order to avoid the effects of the curse of dimensionality. The curse of dimensionality in the k-NN context basically means that Euclid... |
K-nearest neighbors algorithm : Nearest neighbor rules in effect implicitly compute the decision boundary. It is also possible to compute the decision boundary explicitly, and to do so efficiently, so that the computational complexity is a function of the boundary complexity. |
K-nearest neighbors algorithm : Data reduction is one of the most important problems for work with huge data sets. Usually, only some of the data points are needed for accurate classification. Those data are called the prototypes and can be found as follows: Select the class-outliers, that is, training data that are cl... |
K-nearest neighbors algorithm : In k-NN regression, also known as k-NN smoothing, the k-NN algorithm is used for estimating continuous variables. One such algorithm uses a weighted average of the k nearest neighbors, weighted by the inverse of their distance. This algorithm works as follows: Compute the Euclidean or Ma... |
K-nearest neighbors algorithm : The distance to the kth nearest neighbor can also be seen as a local density estimate and thus is also a popular outlier score in anomaly detection. The larger the distance to the k-NN, the lower the local density, the more likely the query point is an outlier. Although quite simple, thi... |
K-nearest neighbors algorithm : A confusion matrix or "matching matrix" is often used as a tool to validate the accuracy of k-NN classification. More robust statistical methods such as likelihood-ratio test can also be applied. |
K-nearest neighbors algorithm : Nearest centroid classifier Closest pair of points problem Nearest neighbor graph Segmentation-based object categorization |
K-nearest neighbors algorithm : Dasarathy, Belur V., ed. (1991). Nearest Neighbor (NN) Norms: NN Pattern Classification Techniques. ISBN 978-0818689307. Shakhnarovich, Gregory; Darrell, Trevor; Indyk, Piotr, eds. (2005). Nearest-Neighbor Methods in Learning and Vision. MIT Press. ISBN 978-0262195478. |
Kernel methods for vector output : Kernel methods are a well-established tool to analyze the relationship between input data and the corresponding output of a function. Kernels encapsulate the properties of functions in a computationally efficient way and allow algorithms to easily swap functions of varying complexity.... |
Kernel methods for vector output : The history of learning vector-valued functions is closely linked to transfer learning- storing knowledge gained while solving one problem and applying it to a different but related problem. The fundamental motivation for transfer learning in the field of machine learning was discusse... |
Kernel methods for vector output : In this context, the supervised learning problem is to learn the function f which best predicts vector-valued outputs y i given inputs (data) x i . f ( x i ) = y i )=\mathbf for i = 1 , … , N x i ∈ X \in , an input space (e.g. X = R p =\mathbb ^ ) y i ∈ R D \in \mathbb ^... |
Kernel methods for vector output : When implementing an algorithm using any of the kernels above, practical considerations of tuning the parameters and ensuring reasonable computation time must be considered. |
Kernel principal component analysis : In the field of multivariate statistics, kernel principal component analysis (kernel PCA) is an extension of principal component analysis (PCA) using techniques of kernel methods. Using a kernel, the originally linear operations of PCA are performed in a reproducing kernel Hilbert ... |
Kernel principal component analysis : Recall that conventional PCA operates on zero-centered data; that is, 1 N ∑ i = 1 N x i = 0 \sum _^\mathbf _=\mathbf , where x i _ is one of the N multivariate observations. It operates by diagonalizing the covariance matrix, C = 1 N ∑ i = 1 N x i x i ⊤ \sum _^\mathbf _\mathb... |
Kernel principal component analysis : To understand the utility of kernel PCA, particularly for clustering, observe that, while N points cannot, in general, be linearly separated in d < N dimensions, they can almost always be linearly separated in d ≥ N dimensions. That is, given N points, x i _ , if we map them to ... |
Kernel principal component analysis : In practice, a large data set leads to a large K, and storing K may become a problem. One way to deal with this is to perform clustering on the dataset, and populate the kernel with the means of those clusters. Since even this method may yield a relatively large K, it is common to ... |
Kernel principal component analysis : Consider three concentric clouds of points (shown); we wish to use kernel PCA to identify these groups. The color of the points does not represent information involved in the algorithm, but only shows how the transformation relocates the data points. First, consider the kernel k ( ... |
Kernel principal component analysis : Kernel PCA has been demonstrated to be useful for novelty detection and image de-noising. |
Kernel principal component analysis : Cluster analysis Nonlinear dimensionality reduction Spectral clustering == References == |
Label propagation algorithm : Label propagation is a semi-supervised algorithm in machine learning that assigns labels to previously unlabeled data points. At the start of the algorithm, a (generally small) subset of the data points have labels (or classifications). These labels are propagated to the unlabeled points t... |
Label propagation algorithm : At initial condition, the nodes carry a label that denotes the community they belong to. Membership in a community changes based on the labels that the neighboring nodes possess. This change is subject to the maximum number of labels within one degree of the nodes. Every node is initialize... |
Label propagation algorithm : Label propagation offers an efficient solution to the challenge of labeling datasets in machine learning by reducing the need for manual labels. Text classification utilizes a graph-based technique, where the nearest neighbor graph is built from network embeddings, and labels are extended ... |
Label propagation algorithm : In contrast with other algorithms label propagation can result in various community structures from the same initial condition. The range of solutions can be narrowed if some nodes are given preliminary labels while others are held unlabelled. Consequently, unlabelled nodes will be more li... |
Label propagation algorithm : Python implementation of label propagation algorithm. |
Lasso (statistics) : In statistics and machine learning, lasso (least absolute shrinkage and selection operator; also Lasso, LASSO or L1 regularization) is a regression analysis method that performs both variable selection and regularization in order to enhance the prediction accuracy and interpretability of the result... |
Lasso (statistics) : Lasso was introduced in order to improve the prediction accuracy and interpretability of regression models. It selects a reduced set of the known covariates for use in a model. Lasso was developed independently in geophysics literature in 1986, based on prior work that used the ℓ 1 penalty for bot... |
Lasso (statistics) : Lasso regularization can be extended to other objective functions such as those for generalized linear models, generalized estimating equations, proportional hazards models, and M-estimators. Given the objective function 1 N ∑ i = 1 N f ( x i , y i , α , β ) \sum _^f(x_,y_,\alpha ,\beta ) the lasso... |
Lasso (statistics) : Lasso variants have been created in order to remedy limitations of the original technique and to make the method more useful for particular problems. Almost all of these focus on respecting or exploiting dependencies among the covariates. Elastic net regularization adds an additional ridge regressi... |
Lasso (statistics) : The loss function of the lasso is not differentiable, but a wide variety of techniques from convex analysis and optimization theory have been developed to compute the solutions path of the lasso. These include coordinate descent, subgradient methods, least-angle regression (LARS), and proximal grad... |
Lasso (statistics) : Choosing the regularization parameter ( λ ) is a fundamental part of lasso. A good value is essential to the performance of lasso since it controls the strength of shrinkage and variable selection, which, in moderation can improve both prediction accuracy and interpretability. However, if the regu... |
Lasso (statistics) : LASSO has been applied in economics and finance, and was found to improve prediction and to select sometimes neglected variables, for example in corporate bankruptcy prediction literature, or high growth firms prediction. |
Lasso (statistics) : Least absolute deviations Model selection Nonparametric regression Tikhonov regularization == References == |
Local outlier factor : In anomaly detection, the local outlier factor (LOF) is an algorithm proposed by Markus M. Breunig, Hans-Peter Kriegel, Raymond T. Ng and Jörg Sander in 2000 for finding anomalous data points by measuring the local deviation of a given data point with respect to its neighbours. LOF shares some co... |
Local outlier factor : The local outlier factor is based on a concept of a local density, where locality is given by k nearest neighbors, whose distance is used to estimate the density. By comparing the local density of an object to the local densities of its neighbors, one can identify regions of similar density, and ... |
Local outlier factor : Let k -distance ( A ) (A) be the distance of the object A to the k-th nearest neighbor. Note that the set of the k nearest neighbors includes all objects at this distance, which can in the case of a "tie" be more than k objects. We denote the set of k nearest neighbors as Nk(A). This distance is ... |
Local outlier factor : Due to the local approach, LOF is able to identify outliers in a data set that would not be outliers in another area of the data set. For example, a point at a "small" distance to a very dense cluster is an outlier, while a point within a sparse cluster might exhibit similar distances to its neig... |
Local outlier factor : The resulting values are quotient-values and hard to interpret. A value of 1 or even less indicates a clear inlier, but there is no clear rule for when a point is an outlier. In one data set, a value of 1.1 may already be an outlier, in another dataset and parameterization (with strong local fluc... |
Logic learning machine : Logic learning machine (LLM) is a machine learning method based on the generation of intelligible rules. LLM is an efficient implementation of the Switching Neural Network (SNN) paradigm, developed by Marco Muselli, Senior Researcher at the Italian National Research Council CNR-IEIIT in Genoa. ... |
Logic learning machine : The Switching Neural Network approach was developed in the 1990s to overcome the drawbacks of the most commonly used machine learning methods. In particular, black box methods, such as multilayer perceptron and support vector machine, had good accuracy but could not provide deep insight into th... |
Logic learning machine : Like other machine learning methods, LLM uses data to build a model able to perform a good forecast about future behaviors. LLM starts from a table including a target variable (output) and some inputs and generates a set of rules that return the output value y corresponding to a given configur... |
Logic learning machine : According to the output type, different versions of the Logic Learning Machine have been developed: Logic Learning Machine for classification, when the output is a categorical variable, which can assume values in a finite set Logic Learning Machine for regression, when the output is an integer ... |
Logic learning machine : Rulex Official Website Machine Learning Engineer |
Loss functions for classification : In machine learning and mathematical optimization, loss functions for classification are computationally feasible loss functions representing the price paid for inaccuracy of predictions in classification problems (problems of identifying which category a particular observation belon... |
Loss functions for classification : Utilizing Bayes' theorem, it can be shown that the optimal f 0 / 1 ∗ ^ , i.e., the one that minimizes the expected risk associated with the zero-one loss, implements the Bayes optimal decision rule for a binary classification problem and is in the form of f 0 / 1 ∗ ( x → ) = ^()\;=\;... |
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