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Multilinear Principal Component Analysis
Within statistics, Multilinear principal component analysis (MPCA) is a multilinear extension of principal component analysis (PCA). MPCA is employed in the analysis of M-way arrays, i.e. a cube or hyper-cube of numbers, also informally referred to as a "data tensor". M-way arrays may be modeled by * linear tensor models such as CANDECOMP/Parafac, or * multilinear tensor models, such as multilinear principal component analysis (MPCA), or multilinear independent component analysis (MICA), etc. The origin of MPCA can be traced back to the Tucker decomposition and Peter Kroonenberg's "3-mode PCA" work.P. M. Kroonenberg and J. de LeeuwPrincipal component analysis of three-mode data by means of alternating least squares algorithms Psychometrika, 45 (1980), pp. 69–97. In 2000, De Lathauwer et al. restated Tucker and Kroonenberg's work in clear and concise numerical computational terms in their SIAM paper entitled "Multilinear Singular Value Decomposition Multilinear may refer to: * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multilinear Algebra
Multilinear algebra is a subfield of mathematics that extends the methods of linear algebra. Just as linear algebra is built on the concept of a vector and develops the theory of vector spaces, multilinear algebra builds on the concepts of ''p''-vectors and multivectors with Grassmann algebras. Origin In a vector space of dimension ''n'', normally only vectors are used. However, according to Hermann Grassmann and others, this presumption misses the complexity of considering the structures of pairs, triplets, and general multi-vectors. With several combinatorial possibilities, the space of multi-vectors has 2''n'' dimensions. The abstract formulation of the determinant is the most immediate application. Multilinear algebra also has applications in the mechanical study of material response to stress and strain with various moduli of elasticity. This practical reference led to the use of the word tensor, to describe the elements of the multilinear space. The extra structure in a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principal Component Analysis
Principal component analysis (PCA) is a popular technique for analyzing large datasets containing a high number of dimensions/features per observation, increasing the interpretability of data while preserving the maximum amount of information, and enabling the visualization of multidimensional data. Formally, PCA is a statistical technique for reducing the dimensionality of a dataset. This is accomplished by linearly transforming the data into a new coordinate system where (most of) the variation in the data can be described with fewer dimensions than the initial data. Many studies use the first two principal components in order to plot the data in two dimensions and to visually identify clusters of closely related data points. Principal component analysis has applications in many fields such as population genetics, microbiome studies, and atmospheric science. The principal components of a collection of points in a real coordinate space are a sequence of p unit vectors, where th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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). 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 of the three or more modes, and the components are linked to each other by a three- (or higher-) way core array. The model parameters are estimated in such a way that, given fixed numbers of components, the modelled data optimally resemble the actual da ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Psychometrika
''Psychometrika'' is the official journal of the Psychometric Society, a professional body devoted to psychometrics and quantitative psychology. The journal covers quantitative methods for 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 a 2019 impact factor of 1.959. History In 1935 LL Thurstone, EL Thorndike and JP Guilford founded ''Psychometrika'' and also the Psychometric Society. Editors-in-chief 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 * Dorothy Adkins * Norman Cliff * Roger Millsap * Shizuhiko Nishisato * Willem J. Heiser * Irini Moustaki ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multilinear Singular Value Decomposition , 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 a subfield of mathematics that extends the methods of linear algebra. Just as linear algebra is built on the concept of a vector and develops the theory of vector spaces, multilinear algebra builds on the concepts of ''p' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Demetri Terzopoulos
Demetri Terzopoulos is an Academy Award winning Greek-Canadian-American computer scientist, university professor, author, and entrepreneur. He is best known for pioneering the physics-based approach to computer graphics and vision that has helped unify these two fields, and for introducing Deformable Models, among them the seminal Active Contour Models, to graphics, vision, medical imaging, and other domains; he is also known for his artificial life research on realistic animal and human modeling and simulation, encompassing musculoskeletal biomechanics, neuromuscular and neuro- sensorimotor control, and artificial intelligence. He has been a professor of computer science, electrical and computer engineering, and mathematics, and has taught courses in computer graphics, computer vision, scientific computing, and artificial intelligence/life at three universities. He is currently a Distinguished Professor and Chancellor's Professor of Computer Science in the Henry Samueli Schoo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
