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65 relations: Autoencoder, Backpropagation, Canonical correlation, Circumstellar disc, Combinatorial optimization, Correlation and dependence, Covariance, CUR matrix approximation, Curse of dimensionality, Data analysis, Data transformation (statistics), Diffusion map, Dimension, Eigenvalues and eigenvectors, Embedding, Feature (machine learning), Feature extraction, Feature selection, Hyperparameter optimization, Information gain in decision trees, Information theory, Isomap, Johnson–Lindenstrauss lemma, K-nearest neighbors algorithm, Kernel method, Kernel principal component analysis, Latent semantic analysis, Linear discriminant analysis, Local tangent space alignment, Locality-sensitive hashing, Machine learning, Matrix (mathematics), Maximally informative dimensions, Methods of detecting exoplanets, MinHash, MIT Press, Multidimensional scaling, Multifactor dimensionality reduction, Multilinear principal component analysis, Multilinear subspace learning, Mutual information, Nature (journal), Nearest neighbor search, Neural network, Neuroscience, Non-negative matrix factorization, Nonlinear dimensionality reduction, Principal component analysis, Random projection, Regression analysis, ..., Restricted Boltzmann machine, Sammon mapping, Semantic mapping (statistics), Semidefinite embedding, Semidefinite programming, Singular-value decomposition, Statistical classification, Statistics, Sufficient dimension reduction, T-distributed stochastic neighbor embedding, Tensor, Time series, Topological data analysis, VLDB, Weighted correlation network analysis. Expand index (15 more) »
Autoencoder
An autoencoder is a type of artificial neural network used to learn efficient data codings in an unsupervised manner.
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Backpropagation
Backpropagation is a method used in artificial neural networks to calculate a gradient that is needed in the calculation of the weights to be used in the network.
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Canonical correlation
In statistics, canonical-correlation analysis (CCA) is a way of inferring information from cross-covariance matrices.
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Circumstellar disc
A circumstellar disc (or circumstellar disk) is a torus, pancake or ring-shaped accumulation of matter composed of gas, dust, planetesimals, asteroids or collision fragments in orbit around a star.
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Combinatorial optimization
In applied mathematics and theoretical computer science, combinatorial optimization is a topic that consists of finding an optimal object from a finite set of objects.
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Correlation and dependence
In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data.
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Covariance
In probability theory and statistics, covariance is a measure of the joint variability of two random variables.
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CUR matrix approximation
A CUR matrix approximation is a set of three matrices that, when multiplied together, closely approximate a given matrix.
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Curse of dimensionality
The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces (often with hundreds or thousands of dimensions) that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience.
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Data analysis
Data analysis is a process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making.
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Data transformation (statistics)
In statistics, data transformation is the application of a deterministic mathematical function to each point in a data set — that is, each data point zi is replaced with the transformed value yi.
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Diffusion map
Diffusion maps is a dimensionality reduction or feature extraction algorithm introduced by Coifman and Lafon which computes a family of embeddings of a data set into Euclidean space (often low-dimensional) whose coordinates can be computed from the eigenvectors and eigenvalues of a diffusion operator on the data.
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Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
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Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
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Embedding
In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.
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Feature (machine learning)
In machine learning and pattern recognition, a feature is an individual measurable property or characteristic of a phenomenon being observed.
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Feature extraction
In machine learning, pattern recognition and in image processing, feature extraction starts from an initial set of measured data and builds derived values (features) intended to be informative and non-redundant, facilitating the subsequent learning and generalization steps, and in some cases leading to better human interpretations.
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Feature selection
In machine learning and statistics, feature selection, also known as variable selection, attribute selection or variable subset selection, is the process of selecting a subset of relevant features (variables, predictors) for use in model construction.
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Hyperparameter optimization
In machine learning, hyperparameter optimization or tuning is the problem of choosing a set of optimal hyperparameters for a learning algorithm.
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Information gain in decision trees
In information theory and machine learning, information gain is a synonym for Kullback–Leibler divergence.
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Information theory
Information theory studies the quantification, storage, and communication of information.
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Isomap
Isomap is a nonlinear dimensionality reduction method.
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Johnson–Lindenstrauss lemma
In mathematics, the Johnson–Lindenstrauss lemma is a result named after William B. Johnson and Joram Lindenstrauss concerning low-distortion embeddings of points from high-dimensional into low-dimensional Euclidean space.
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K-nearest neighbors algorithm
In pattern recognition, the k-nearest neighbors algorithm (k-NN) is a non-parametric method used for classification and regression.
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Kernel method
In machine learning, kernel methods are a class of algorithms for pattern analysis, whose best known member is the support vector machine (SVM).
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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.
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Latent semantic analysis
Latent semantic analysis (LSA) is a technique in natural language processing, in particular distributional semantics, of analyzing relationships between a set of documents and the terms they contain by producing a set of concepts related to the documents and terms.
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Linear discriminant analysis
Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics, pattern recognition and machine learning to find a linear combination of features that characterizes or separates two or more classes of objects or events.
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Local tangent space alignment
Local tangent space alignment (LTSA) is a method for manifold learning, which can efficiently learn a nonlinear embedding into low-dimensional coordinates from high-dimensional data, and can also reconstruct high-dimensional coordinates from embedding coordinates.
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Locality-sensitive hashing
Locality-sensitive hashing (LSH) reduces the dimensionality of high-dimensional data.
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Machine learning
Machine learning is a subset of artificial intelligence in the field of computer science that often uses statistical techniques to give computers the ability to "learn" (i.e., progressively improve performance on a specific task) with data, without being explicitly programmed.
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Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
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Maximally informative dimensions
Maximally informative dimensions is a dimensionality reduction technique used in the statistical analyses of neural responses.
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Methods of detecting exoplanets
Any planet is an extremely faint light source compared to its parent star.
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MinHash
In computer science and data mining, MinHash (or the min-wise independent permutations locality sensitive hashing scheme) is a technique for quickly estimating how similar two sets are.
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MIT Press
The MIT Press is a university press affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts (United States).
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Multidimensional scaling
Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a dataset.
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Multifactor dimensionality reduction
Multifactor dimensionality reduction (MDR) is a statistical approach, also used in machine learning automatic approaches, for detecting and characterizing combinations of attributes or independent variables that interact to influence a dependent or class variable.
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Multilinear principal component analysis
Multilinear principal component analysis (MPCA) is a multilinear extension of principal component analysis (PCA).
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Multilinear subspace learning
Multilinear subspace learning is an approach to dimensionality reduction.
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Mutual information
In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables.
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Nature (journal)
Nature is a British multidisciplinary scientific journal, first published on 4 November 1869.
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Nearest neighbor search
Nearest neighbor search (NNS), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest (or most similar) to a given point.
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Neural network
The term neural network was traditionally used to refer to a network or circuit of neurons.
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Neuroscience
Neuroscience (or neurobiology) is the scientific study of the nervous system.
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Non-negative matrix factorization
Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix is factorized into (usually) two matrices and, with the property that all three matrices have no negative elements.
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Nonlinear dimensionality reduction
High-dimensional data, meaning data that requires more than two or three dimensions to represent, can be difficult to interpret.
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Principal component analysis
Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components.
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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.
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Regression analysis
In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships among variables.
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Restricted Boltzmann machine
A restricted Boltzmann machine (RBM) is a generative stochastic artificial neural network that can learn a probability distribution over its set of inputs.
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Sammon mapping
Sammon mapping or Sammon projection is an algorithm that maps a high-dimensional space to a space of lower dimensionality (see multidimensional scaling) by trying to preserve the structure of inter-point distances in high-dimensional space in the lower-dimension projection.
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Semantic mapping (statistics)
Semantic mapping (SM) is a method in statistics for dimensionality reduction that can be used in a set of multidimensional vectors of features to extract a few new features that preserves the main data characteristics.
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Semidefinite embedding
Semidefinite embedding (SDE) or maximum variance unfolding (MVU) is an algorithm in computer science that uses semidefinite programming to perform non-linear dimensionality reduction of high-dimensional vectorial input data.
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Semidefinite programming
Semidefinite programming (SDP) is a subfield of convex optimization concerned with the optimization of a linear objective function (a user-specified function that the user wants to minimize or maximize) over the intersection of the cone of positive semidefinite matrices with an affine space, i.e., a spectrahedron.
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Singular-value decomposition
In linear algebra, the singular-value decomposition (SVD) is a factorization of a real or complex matrix.
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Statistical classification
In machine learning and statistics, classification is the problem of identifying to which of a set of categories (sub-populations) a new observation belongs, on the basis of a training set of data containing observations (or instances) whose category membership is known.
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Statistics
Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.
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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.
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T-distributed stochastic neighbor embedding
T-distributed Stochastic Neighbor Embedding (t-SNE) is a machine learning algorithm for visualization developed by Laurens van der Maaten and Geoffrey Hinton.
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Tensor
In mathematics, tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.
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Time series
A time series is a series of data points indexed (or listed or graphed) in time order.
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Topological data analysis
In applied mathematics, topological data analysis (TDA) is an approach to the analysis of datasets using techniques from topology.
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VLDB
VLDB is an annual conference held by the non-profit Very Large Data Base Endowment Inc. The mission of VLDB is to promote and exchange scholarly work in databases and related fields throughout the world.
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Weighted correlation network analysis
Weighted correlation network analysis, also known as weighted gene co-expression network analysis (WGCNA), is a widely used data mining method especially for studying biological networks based on pairwise correlations between variables.
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References
[1] https://en.wikipedia.org/wiki/Dimensionality_reduction
