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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.M. A. O. Vasilescu, D. Terzopoulos (2003"Multilinear Subspace Analysis of Image Ensembles" "Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR’03), Madison, WI, June, 2003"M. A. O. Vasilescu, D. Terzopoulos (2002"Multilinear Analysis of Image Ensembles: TensorFaces" Proc. 7th European Conference on Computer Vision (ECCV'02), Copenhagen, Denmark, May, 2002M. A. O. Vasilescu,(2002"Human Motion Signatures: Analysis, Synthesis, Recognition" "Proceedings of International Conference on Pattern Recognition (ICPR 2002), Vol. 3, Quebec City, Canada, Aug, 2002, 456–460." The Dimensionality reduction can be performed on a data tensor that contains a collection of observations that have been vectorized, or observations that are treated as matrices and concatenated into a data tensor.X. He, D. Cai, P. NiyogiTensor s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Video Represented As A Third-order Tensor
Video is an Electronics, electronic medium for the recording, copying, playback, broadcasting, and display of moving picture, moving image, visual Media (communication), media. Video was first developed for mechanical television systems, which were quickly replaced by cathode-ray tube (CRT) systems, which, in turn, were replaced by flat-panel displays of several types. Video systems vary in display resolution, Display aspect ratio, aspect ratio, refresh rate, color capabilities, and other qualities. Analog and digital variants exist and can be carried on a variety of media, including radio broadcasts, magnetic tape, optical discs, Video file format, computer files, and Streaming media, network streaming. Etymology The word ''video'' comes from the Latin verb ''video,'' meaning to see or ''videre''. And as a noun, "that which is displayed on a (television) screen," History Analog video Video developed from facsimile systems developed in the mid-19th century. Early mecha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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IEEE Conference On Computer Vision And Pattern Recognition
The Institute of Electrical and Electronics Engineers (IEEE) is an American 501(c)(3) public charity professional organization for electrical engineering, electronics engineering, and other related disciplines. The IEEE has a corporate office in New York City and an operations center in Piscataway, New Jersey. The IEEE was formed in 1963 as an amalgamation of the American Institute of Electrical Engineers and the Institute of Radio Engineers. History The IEEE traces its founding to 1884 and the American Institute of Electrical Engineers. In 1912, the rival Institute of Radio Engineers was formed. Although the AIEE was initially larger, the IRE attracted more students and was larger by the mid-1950s. The AIEE and IRE merged in 1963. The IEEE is headquartered in New York City, but most business is done at the IEEE Operations Center in Piscataway, New Jersey, opened in 1975. The Australian Section of the IEEE existed between 1972 and 1985, after which it split into state- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Multilinear Algebra
Multilinear algebra is the study of Function (mathematics), functions with multiple vector space, vector-valued Argument of a function, arguments, with the functions being Linear map, linear maps with respect to each argument. It involves concepts such as Matrix (mathematics), matrices, tensors, multivectors, System of linear equations, systems of linear equations, Higher-dimensional space, higher-dimensional spaces, Determinant, determinants, inner product, inner and outer product, outer products, and Dual space, dual spaces. It is a mathematical tool used in engineering, machine learning, physics, and mathematics. Origin While many theoretical concepts and applications involve Vector space, single vectors, mathematicians such as Hermann Grassmann considered structures involving pairs, triplets, and multivectors that generalize Vector (mathematics and physics), vectors. With multiple combinational possibilities, the space of multivectors expands to 2''n'' dimensions, where ''n'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Sandia National Laboratories
Sandia National Laboratories (SNL), also known as Sandia, is one of three research and development laboratories of the United States Department of Energy's National Nuclear Security Administration (NNSA). Headquartered in Kirtland Air Force Base in Albuquerque, New Mexico, it has a second principal facility next to Lawrence Livermore National Laboratory in Livermore, California, and a test facility in Waimea, Kauai, Hawaii. Sandia is owned by the U.S. federal government but privately managed and operated by National Technology and Engineering Solutions of Sandia, a wholly owned subsidiary of Honeywell International. Established in 1949, SNL is a "multimission laboratory" with the primary goal of advancing U.S. national security by developing various science-based technologies. Its work spans roughly 70 areas of activity, including nuclear deterrence, arms control, nonproliferation, hazardous waste disposal, and climate change. Sandia hosts a wide variety of research i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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PARAFAC
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. Computing this decomposition is an open problem. Canonical polyadic decomposition (CPD) is a variant of the tensor rank decomposition, in which the tensor is approximated as a sum of ''K'' rank-1 tensors for a user-specified ''K''. The CP decomposition has found some applications in linguistics and chemometrics. It was introduced by Frank Lauren Hitchcock in 1927 and later rediscovered several times, notably in psychometrics. The CP decomposition is referred to as CANDECOMP, PARAFAC, or CANDECOMP/PARAFAC (CP). Note that the PARAFAC2 rank decomposition is a variation of the CP decomposition. Another popular generalization of the matrix SVD known as the higher-order singular value decomposition computes orthonormal mode matrices and has found applications in econometrics, signal processing, computer vision, co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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CP Decomposition
CP, cp. or its variants may refer to: Arts, entertainment, and media * Cariyapitaka (Cp), a canonical Buddhist story collection * The Canadian Press, a Canadian news agency * Child pornography * '' The Christian Post'', an American newspaper * Competitive programming * '' Club Penguin'', a now defunct online multiplayer game * Combat power, used in Pokémon Go to indicate how strong a Pokémon is in battle Enterprises Transportation companies * Canadian Airlines (1987–2001) (IATA airline code CP) * Canadian Pacific Railway, reporting mark CP * Central Pacific Railroad, a network of lines between California and Utah, US * , a French public railway company * , a Portuguese state-owned train company * CP Air or Canadian Pacific Air Lines (1942–1987), a Canadian airline * CP Ships, a Canadian shipping company, part of TUI Group * Cathay Pacific, a Hong Kong–based major airline Other enterprises * C.P. Company, an Italian apparel brand * Cedar Point, an amusement p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Psychometrika
''Psychometrika'' is the official journal of the Psychometric Society, a professional body dedicated to psychometrics and quantitative psychology. The journal focuses on quantitative methods for the measurement and evaluation of human behavior, including statistical methods and other mathematical techniques. Past editors include Marion Richardson, Dorothy Adkins, Norman Cliff, and Willem J. Heiser. According to ''Journal Citation Reports'', the journal had an impact factor of 2.9 in 2023. History In 1935, LL Thurstone, EL Thorndike and JP Guilford founded ''Psychometrika'' and also the Psychometric Society. Editors-in-chief The current editor of the journal is Sandip Sinharay of Educational Testing Service. The complete list of editor-in-chief of Psychometrika can be found at: https://www.psychometricsociety.org/content/past-psychometrika-editors The following is a subset of persons who have been editor-in-chief of Psychometrika: * Paul Horst * Albert K. Kurtz * Dorot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Tucker Decomposition
In mathematics, Tucker decomposition decomposes a tensor into a set of matrices and one small core tensor. It is named after Ledyard R. Tucker although it goes back to Hitchcock in 1927. Initially described as a three-mode extension of factor analysis and principal component analysis it may actually be generalized to higher mode analysis, which is also called higher-order singular value decomposition (HOSVD) or the M-mode SVD. The algorithm to which the literature typically refers when discussing the Tucker decomposition or the HOSVD is the M-mode SVD algorithm introduced by Vasilescu and Terzopoulos, but misattributed to Tucker or De Lathauwer etal. It may be regarded as a more flexible PARAFAC (parallel factor analysis) model. In PARAFAC the core tensor is restricted to be "diagonal". In practice, Tucker decomposition is used as a modelling tool. For instance, it is used to model three-way (or higher way) data by means of relatively small numbers of components for each o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Higher-order Singular Value Decomposition
In multilinear algebra, the higher-order singular value decomposition (HOSVD) of a tensor is a specific orthogonal Tucker decomposition. It may be regarded as one type of generalization of the matrix singular value decomposition. It has applications in computer vision, computer graphics, machine learning, scientific computing, and signal processing. Some aspects can be traced as far back as F. L. Hitchcock in 1928, but it was L. R. Tucker who developed for third-order tensors the general Tucker decomposition in the 1960s, further advocated by Lieven De Lathauwer, L. De Lathauwer ''et al.'' , or advocated by Vasilescu and Terzopoulos. Although the term HOSVD was coined by De Lathauwer, the algorithm most commonly referred to as the Tucker or Higher-Order Singular Value Decomposition (HOSVD) in the literature was originally introduced by Vasilescu and Terzopoulos under the name M-mode SVD.M. A. O. Vasilescu, D. Terzopoulos (2002), "Multilinear Analysis of Image Ensembles: TensorFace ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Canonical Correlation Analysis
In statistics, canonical-correlation analysis (CCA), also called canonical variates analysis, is a way of inferring information from cross-covariance matrices. If we have two vectors ''X'' = (''X''1, ..., ''X''''n'') and ''Y'' = (''Y''1, ..., ''Y''''m'') of random variables, and there are correlations among the variables, then canonical-correlation analysis will find linear combinations of ''X'' and ''Y'' that have a maximum correlation with each other. T. R. Knapp notes that "virtually all of the commonly encountered parametric tests of significance can be treated as special cases of canonical-correlation analysis, which is the general procedure for investigating the relationships between two sets of variables." The method was first introduced by Harold Hotelling in 1936, although in the context of angles between flats the mathematical concept was published by Camille Jordan in 1875. CCA is now a cornerstone of multivariate statistics a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Independent Component Analysis
In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate statistics, multivariate signal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and that the subcomponents are Statistical independence, statistically independent from each other. ICA was invented by Jeanny Hérault and Christian Jutten in 1985. ICA is a special case of blind source separation. A common example application of ICA is the "cocktail party problem" of listening in on one person's speech in a noisy room. Introduction Independent component analysis attempts to decompose a multivariate signal into independent non-Gaussian signals. As an example, sound is usually a signal that is composed of the numerical addition, at each time t, of signals from several sources. The question then is whether it is possible to separate these contributing sources from the observed total signal. When the statistical independence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Multilinear Independent Component Analysis , a field of mathematics
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Multilinear may refer to: * Multilinear form, a type of mathematical function from a vector space to the underlying field * Multilinear map, a type of mathematical function between vector spaces * Multilinear algebra Multilinear algebra is the study of Function (mathematics), functions with multiple vector space, vector-valued Argument of a function, arguments, with the functions being Linear map, linear maps with respect to each argument. It involves concept ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |