Non-negative matrix factorization, the Glossary

Table of Contents

1. 103 relations: Acta Neuropathologica, Active-set method, Algorithm, Amnon Shashua, Association for Computing Machinery, Astronomy, Atmospheric Environment, Audio signal processing, Bayesian network, Bioinformatics, Bioinformatics (journal), Chemometrics, Chemometrics and Intelligent Laboratory Systems, Circumstellar disc, Collaborative filtering, Computational and Mathematical Organization Theory, Computer vision, Convex combination, Data stream, Dimensionality reduction, Disk sector, DNA methylation, Document clustering, Document-term matrix, Drug repositioning, English Wikipedia, Enron, Exoplanet, Gaussian noise, Gene expression, Generalized permutation matrix, Genetic admixture, Genetics (journal), Gradient descent, IEEE Journal on Selected Areas in Communications, IEEE Transactions on Nuclear Science, Imputation (statistics), Institute of Electrical and Electronics Engineers, Invertible matrix, Journal of Cerebral Blood Flow & Metabolism, Journal of Computational and Graphical Statistics, K-means clustering, Kernel (image processing), Kosambi–Karhunen–Loève theorem, Kullback–Leibler divergence, Lasso (statistics), Latent class model, Linear algebra, Linearity, List of Hindawi academic journals, ... Expand index (53 more) »

2. Factorization

Acta Neuropathologica

Acta Neuropathologica is a monthly peer-reviewed scientific journal covering all aspects of neuropathology published by Springer Science+Business Media.

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Active-set method

In mathematical optimization, the active-set method is an algorithm used to identify the active constraints in a set of inequality constraints.

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Algorithm

In mathematics and computer science, an algorithm is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation.

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Amnon Shashua

Amnon Shashua (born May 26, 1960) is an Israeli computer scientist, businessman and philanthropist.

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Association for Computing Machinery

The Association for Computing Machinery (ACM) is a US-based international learned society for computing.

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Astronomy

Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos.

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Atmospheric Environment

Atmospheric Environment is a peer-reviewed scientific journal covering research pertaining to air pollution and other ways humans and natural forces affect the Earth's atmosphere.

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Audio signal processing

Audio signal processing is a subfield of signal processing that is concerned with the electronic manipulation of audio signals.

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Bayesian network

A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG).

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Bioinformatics

Bioinformatics is an interdisciplinary field of science that develops methods and software tools for understanding biological data, especially when the data sets are large and complex.

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Bioinformatics (journal)

Bioinformatics is a biweekly peer-reviewed scientific journal covering research and software in bioinformatics and computational biology.

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Chemometrics

Chemometrics is the science of extracting information from chemical systems by data-driven means.

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Chemometrics and Intelligent Laboratory Systems

Chemometrics and Intelligent Laboratory Systems is a peer-reviewed scientific journal sponsored by the Chemometrics Society and published since 1986 by Elsevier.

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Circumstellar disc

A circumstellar disc (or circumstellar disk) is a torus, pancake or ring-shaped accretion disk of matter composed of gas, dust, planetesimals, asteroids, or collision fragments in orbit around a star.

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Collaborative filtering

Collaborative filtering (CF) is a technique used by recommender systems.

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Computational and Mathematical Organization Theory

Computational and Mathematical Organization Theory is a quarterly double-blind peer-reviewed scientific journal covering the field of organization theory.

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Computer vision

Computer vision tasks include methods for acquiring, processing, analyzing and understanding digital images, and extraction of high-dimensional data from the real world in order to produce numerical or symbolic information, e.g. in the forms of decisions.

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Convex combination

In convex geometry and vector algebra, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points in an affine space) where all coefficients are non-negative and sum to 1.

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Data stream

In connection-oriented communication, a data stream is the transmission of a sequence of digitally encoded signals to convey information.

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Dimensionality reduction

Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension.

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Disk sector

In computer disk storage, a sector is a subdivision of a track on a magnetic disk or optical disc.

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DNA methylation

DNA methylation is a biological process by which methyl groups are added to the DNA molecule.

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Document clustering

Document clustering (or text clustering) is the application of cluster analysis to textual documents.

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Document-term matrix

A document-term matrix is a mathematical matrix that describes the frequency of terms that occur in each document in a collection.

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Drug repositioning

Drug repositioning (also called drug repurposing) involves the investigation of existing drugs for new therapeutic purposes.

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English Wikipedia

The English Wikipedia is the primary English-language edition of Wikipedia, an online encyclopedia.

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Enron

Enron Corporation was an American energy, commodities, and services company based in Houston, Texas.

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Exoplanet

An exoplanet or extrasolar planet is a planet outside the Solar System.

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Gaussian noise

In signal processing theory, Gaussian noise, named after Carl Friedrich Gauss, is a kind of signal noise that has a probability density function (pdf) equal to that of the normal distribution (which is also known as the Gaussian distribution).

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Gene expression

Gene expression is the process by which information from a gene is used in the synthesis of a functional gene product that enables it to produce end products, proteins or non-coding RNA, and ultimately affect a phenotype.

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Generalized permutation matrix

In mathematics, a generalized permutation matrix (or monomial matrix) is a matrix with the same nonzero pattern as a permutation matrix, i.e. there is exactly one nonzero entry in each row and each column.

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Genetic admixture

Genetic admixture occurs when previously isolated populations interbreed resulting in a population that is descended from multiple sources.

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Genetics (journal)

Genetics is a monthly scientific journal publishing investigations bearing on heredity, genetics, biochemistry and molecular biology.

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Gradient descent

Gradient descent is a method for unconstrained mathematical optimization.

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IEEE Journal on Selected Areas in Communications

The IEEE Journal on Selected Areas in Communications is a monthly peer-reviewed scientific journal published by the IEEE Communications Society that focuses on telecommunications.

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IEEE Transactions on Nuclear Science

IEEE Transactions on Nuclear Science is a peer-reviewed scientific journal published monthly by the IEEE.

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Imputation (statistics)

In statistics, imputation is the process of replacing missing data with substituted values.

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Institute of Electrical and Electronics Engineers

The Institute of Electrical and Electronics Engineers (IEEE) is an American 501(c)(3) professional association for electronics engineering, electrical engineering, and other related disciplines.

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Invertible matrix

In linear algebra, an -by- square matrix is called invertible (also nonsingular, nondegenerate or rarely regular) if there exists an -by- square matrix such that\mathbf. Non-negative matrix factorization and invertible matrix are linear algebra and matrix theory.

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The Journal of Cerebral Blood Flow & Metabolism is a monthly peer-reviewed medical journal the official journal of the International Society for Cerebral Blood Flow & Metabolism and publishes peer-reviewed research and review papers.

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Journal of Computational and Graphical Statistics

The Journal of Computational and Graphical Statistics is a quarterly peer-reviewed scientific journal published by Taylor & Francis on behalf of the American Statistical Association.

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K-means clustering

k-means clustering is a method of vector quantization, originally from signal processing, that aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean (cluster centers or cluster centroid), serving as a prototype of the cluster.

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Kernel (image processing)

In image processing, a kernel, convolution matrix, or mask is a small matrix used for blurring, sharpening, embossing, edge detection, and more.

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Kosambi–Karhunen–Loève theorem

In the theory of stochastic processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem (after Damodar Dharmananda Kosambi) states that a stochastic process can be represented as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function on a bounded interval.

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Kullback–Leibler divergence

In mathematical statistics, the Kullback–Leibler (KL) divergence (also called relative entropy and I-divergence), denoted D_\text(P \parallel Q), is a type of statistical distance: a measure of how one probability distribution is different from a second, reference probability distribution.

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Lasso (statistics)

In statistics and machine learning, lasso (least absolute shrinkage and selection operator; also Lasso or LASSO) is a regression analysis method that performs both variable selection and regularization in order to enhance the prediction accuracy and interpretability of the resulting statistical model. Non-negative matrix factorization and lasso (statistics) are machine learning algorithms.

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Latent class model

In statistics, a latent class model (LCM) is a model for clustering multivariate discrete data.

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Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices.

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Linearity

In mathematics, the term linear is used in two distinct senses for two different properties.

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List of Hindawi academic journals

This is a list of academic journals published by Hindawi.

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Loss function

In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event.

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Matrix (mathematics)

In mathematics, a matrix (matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object.

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Matrix decomposition

In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. Non-negative matrix factorization and matrix decomposition are factorization and matrix theory.

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Matrix norm

In the field of mathematics, norms are defined for elements within a vector space. Non-negative matrix factorization and Matrix norm are linear algebra.

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Matrix of ones

In mathematics, a matrix of ones or all-ones matrix has every entry equal to one.

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Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data.

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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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MIT Press

The MIT Press is a university press affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts.

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Multilinear algebra

Multilinear algebra is the study of functions with multiple vector-valued arguments, with the functions being linear maps with respect to each argument. Non-negative matrix factorization and Multilinear algebra are linear algebra.

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Multilinear subspace learning

Multilinear subspace learning is an approach for disentangling the causal factor of data formation and performing dimensionality reduction.

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Multiplicative weight update method

The multiplicative weights update method is an algorithmic technique most commonly used for decision making and prediction, and also widely deployed in game theory and algorithm design.

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Multivariate statistics

Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e., multivariate random variables.

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Nature (journal)

Nature is a British weekly scientific journal founded and based in London, England.

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Neural coding

Neural coding (or neural representation) is a neuroscience field concerned with characterising the hypothetical relationship between the stimulus and the neuronal responses, and the relationship among the electrical activities of the neurons in the ensemble.

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Neural Computation (journal)

Neural Computation is a monthly peer-reviewed scientific journal covering all aspects of neural computation, including modeling the brain and the design and construction of neurally-inspired information processing systems.

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Neurocomputing (journal)

Neurocomputing is a peer-reviewed scientific journal covering research on artificial intelligence, machine learning, and neural computation.

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NeuroImage

NeuroImage is a peer-reviewed scientific journal covering research on neuroimaging, including functional neuroimaging and functional human brain mapping.

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Non-negative least squares

In mathematical optimization, the problem of non-negative least squares (NNLS) is a type of constrained least squares problem where the coefficients are not allowed to become negative.

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Nonnegative matrix

In mathematics, a nonnegative matrix, written is a matrix in which all the elements are equal to or greater than zero, that is, A positive matrix is a matrix in which all the elements are strictly greater than zero.

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Nonnegative rank (linear algebra)

In linear algebra, the nonnegative rank of a nonnegative matrix is a concept similar to the usual linear rank of a real matrix, but adding the requirement that certain coefficients and entries of vectors/matrices have to be nonnegative. Non-negative matrix factorization and nonnegative rank (linear algebra) are linear algebra.

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NP-completeness

In computational complexity theory, a problem is NP-complete when.

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Parallel computing

Parallel computing is a type of computation in which many calculations or processes are carried out simultaneously.

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Pattern Recognition Letters

Pattern Recognition Letters is a peer-reviewed scientific journal that is published by North Holland, an imprint of Elsevier, on behalf of the International Association for Pattern Recognition.

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Permutation

In mathematics, a permutation of a set can mean one of two different things.

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PLOS Computational Biology

PLOS Computational Biology is a monthly peer-reviewed open access scientific journal covering computational biology.

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PLOS One

PLOS One (stylized PLOS ONE, and formerly PLoS ONE) is a peer-reviewed open access mega journal published by the Public Library of Science (PLOS) since 2006.

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Population genetics

Population genetics is a subfield of genetics that deals with genetic differences within and among populations, and is a part of evolutionary biology.

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Positron emission tomography

Positron emission tomography (PET) is a functional imaging technique that uses radioactive substances known as radiotracers to visualize and measure changes in metabolic processes, and in other physiological activities including blood flow, regional chemical composition, and absorption.

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Principal component analysis

Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing.

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Probabilistic latent semantic analysis

Probabilistic latent semantic analysis (PLSA), also known as probabilistic latent semantic indexing (PLSI, especially in information retrieval circles) is a statistical technique for the analysis of two-mode and co-occurrence data.

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PubMed

PubMed is a free database including primarily the MEDLINE database of references and abstracts on life sciences and biomedical topics.

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Quadratic programming

Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions.

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Recommender system

A recommender system, or a recommendation system (sometimes replacing system with terms such as platform, engine, or algorithm), is a subclass of information filtering system that provides suggestions for items that are most pertinent to a particular user.

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Regularization (mathematics)

In mathematics, statistics, finance, and computer science, particularly in machine learning and inverse problems, regularization is a process that changes the result answer to be "simpler".

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Science Bulletin

Science Bulletin is a multidisciplinary scientific journal co-sponsored by the Chinese Academy of Sciences and the National Natural Science Foundation of China.

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Scientific journal

In academic publishing, a scientific journal is a periodical publication designed to further the progress of science by disseminating new research findings to the scientific community.

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Sebastian Seung

Hyunjune Sebastian Seung (English: /sung/ or) is President at Samsung Electronics & Head of Samsung Research and Anthony B. Evnin Professor in the Princeton Neuroscience Institute and Department of Computer Science.

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SIAM Journal on Matrix Analysis and Applications

The SIAM Journal on Matrix Analysis and Applications (until 1989: SIAM Journal on Algebraic and Discrete Methods) is a peer-reviewed scientific journal covering matrix analysis and its applications.

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SIAM Journal on Scientific Computing

The SIAM Journal on Scientific Computing (SISC), formerly SIAM Journal on Scientific & Statistical Computing, is a scientific journal focusing on the research articles on numerical methods and techniques for scientific computation.

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Single-photon emission computed tomography

Single-photon emission computed tomography (SPECT, or less commonly, SPET) is a nuclear medicine tomographic imaging technique using gamma rays.

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Singular value decomposition

In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix into a rotation, followed by a rescaling followed by another rotation. Non-negative matrix factorization and singular value decomposition are linear algebra and matrix theory.

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Sparse matrix

In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero.

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Support vector machine

In machine learning, support vector machines (SVMs, also support vector networks) are supervised max-margin models with associated learning algorithms that analyze data for classification and regression analysis.

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Technometrics

Technometrics is a journal of statistics for the physical, chemical, and engineering sciences, published quarterly since 1959 by the American Society for Quality and the American Statistical Association.

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Tensor

In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space.

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Tensor decomposition

In multilinear algebra, a tensor decomposition is any scheme for expressing a "data tensor" (M-way array) as a sequence of elementary operations acting on other, often simpler tensors.

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Tensor rank decomposition

In multilinear algebra, the tensor rank decomposition or rank-R decomposition is the decomposition of a tensor as a sum of R rank-1 tensors, where R is minimal.

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Tensor software

Tensor software is a class of mathematical software designed for manipulation and calculation with tensors.

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Text mining

Text mining, text data mining (TDM) or text analytics is the process of deriving high-quality information from text.

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Total variation

In mathematics, the total variation identifies several slightly different concepts, related to the (local or global) structure of the codomain of a function or a measure.

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Vector quantization

Vector quantization (VQ) is a classical quantization technique from signal processing that allows the modeling of probability density functions by the distribution of prototype vectors.

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Wiener filter

In signal processing, the Wiener filter is a filter used to produce an estimate of a desired or target random process by linear time-invariant (LTI) filtering of an observed noisy process, assuming known stationary signal and noise spectra, and additive noise.

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Wikimania

Wikimania is the Wikimedia movement's annual conference, organized by volunteers and hosted by the Wikimedia Foundation.

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See also

Factorization

• Aurifeuillean factorization
• Dedekind domain
• Factorization
• Factorization of polynomials
• Fundamental theorem of arithmetic
• Fundamental theorem of ideal theory in number fields
• Graph factorization
• Integer factorization
• Integer factorization algorithms
• Lie group decomposition
• Matrix decomposition
• Non-negative matrix factorization
• Sophie Germain's identity
• Sufficient statistic
• Supernatural number
• Unique factorization domain

References

[1] https://en.wikipedia.org/wiki/Non-negative_matrix_factorization

Also known as Algorithms for non-negative matrix factorization, Approximate nonnegative matrix factorization, NNMF, Non-negative matrix decomposition, Nonnegative matrix decomposition, Nonnegative matrix factorization, Online NMF, Positive matrix factorization, Self modeling curve resolution.

, Loss function, Matrix (mathematics), Matrix decomposition, Matrix norm, Matrix of ones, Maximum likelihood estimation, Methods of detecting exoplanets, MIT Press, Multilinear algebra, Multilinear subspace learning, Multiplicative weight update method, Multivariate statistics, Nature (journal), Neural coding, Neural Computation (journal), Neurocomputing (journal), NeuroImage, Non-negative least squares, Nonnegative matrix, Nonnegative rank (linear algebra), NP-completeness, Parallel computing, Pattern Recognition Letters, Permutation, PLOS Computational Biology, PLOS One, Population genetics, Positron emission tomography, Principal component analysis, Probabilistic latent semantic analysis, PubMed, Quadratic programming, Recommender system, Regularization (mathematics), Science Bulletin, Scientific journal, Sebastian Seung, SIAM Journal on Matrix Analysis and Applications, SIAM Journal on Scientific Computing, Single-photon emission computed tomography, Singular value decomposition, Sparse matrix, Support vector machine, Technometrics, Tensor, Tensor decomposition, Tensor rank decomposition, Tensor software, Text mining, Total variation, Vector quantization, Wiener filter, Wikimania.