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Also known as: UTV decomposition, ULV decomposition, URV decomposition. Applicable to: m-by-n matrix A. Decomposition: =, where T is a triangular matrix, and U and V are unitary matrices. Comment: Similar to the singular value decomposition and to the Schur decomposition.
In Learning the parts of objects by non-negative matrix factorization Lee and Seung [43] proposed NMF mainly for parts-based decomposition of images. It compares NMF to vector quantization and principal component analysis , and shows that although the three techniques may be written as factorizations, they implement different constraints and ...
In recent years a number of neural and deep-learning techniques have been proposed, some of which generalize traditional Matrix factorization algorithms via a non-linear neural architecture. [19] While deep learning has been applied to many different scenarios: context-aware, sequence-aware, social tagging etc. its real effectiveness when used ...
Whitening a data matrix follows the same transformation as for random variables. An empirical whitening transform is obtained by estimating the covariance (e.g. by maximum likelihood) and subsequently constructing a corresponding estimated whitening matrix (e.g. by Cholesky decomposition).
Maximum likelihood estimation (MLE) is a standard statistical tool for finding parameter values (e.g. the unmixing matrix ) that provide the best fit of some data (e.g., the extracted signals ) to a given a model (e.g., the assumed joint probability density function (pdf) of source signals).
In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced / ʃ ə ˈ l ɛ s k i / shə-LES-kee) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations.
In data science, dynamic mode decomposition (DMD) is a dimensionality reduction algorithm developed by Peter J. Schmid and Joern Sesterhenn in 2008. [ 1 ] [ 2 ] Given a time series of data, DMD computes a set of modes, each of which is associated with a fixed oscillation frequency and decay/growth rate.
The first idea behind the Proper Orthogonal Decomposition (POD), as it was originally formulated in the domain of fluid dynamics to analyze turbulences, is to decompose a random vector field u(x, t) into a set of deterministic spatial functions Φ k (x) modulated by random time coefficients a k (t) so that: