The matrix ridge approximation: algorithms and applications

We are concerned with an approximation problem for a symmetric positive semidefinite matrix due to motivation from a class of nonlinear machine learning methods. We discuss an approximation approach that we call matrix ridge approximation . In particular, we define the matrix ridge approximation as...

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Vydáno v:	Machine learning Ročník 97; číslo 3; s. 227 - 258
Hlavní autor:	Zhang, Zhihua
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.12.2014 Springer Springer Nature B.V
Témata:	Algebra Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Approximation Artificial Intelligence Computer Science Computer science; control theory; systems Control Data processing. List processing. Character string processing Exact sciences and technology Iterative methods Linear and multilinear algebra, matrix theory Machine learning Machinery Mathematical analysis Mathematical models Mathematics Matrix Mechatronics Memory organisation. Data processing Natural Language Processing (NLP) Regression Ridges Robotics Sciences and techniques of general use Simulation and Modeling Software Theoretical computing Expectation maximization algorithms Incomplete matrix factorization Probabilistic models Positive semidefinite matrices Matrix ridge approximation Cluster analysis Iterative method Matrix factorization Approximation algorithm Multivariate analysis Modeling Multidimensional analysis Data analysis Spectral method Probabilistic interpretation Probabilistic approach Empirical method Latent variable model Regression analysis Matrix decomposition Symmetric matrix Positive semidefinite matrix Non linear effect EM algorithm Artificial intelligence
ISSN:	0885-6125, 1573-0565
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Shrnutí:	We are concerned with an approximation problem for a symmetric positive semidefinite matrix due to motivation from a class of nonlinear machine learning methods. We discuss an approximation approach that we call matrix ridge approximation . In particular, we define the matrix ridge approximation as an incomplete matrix factorization plus a ridge term. Moreover, we present probabilistic interpretations using a normal latent variable model and a Wishart model for this approximation approach. The idea behind the latent variable model in turn leads us to an efficient EM iterative method for handling the matrix ridge approximation problem. Finally, we illustrate the applications of the approximation approach in multivariate data analysis. Empirical studies in spectral clustering and Gaussian process regression show that the matrix ridge approximation with the EM iteration is potentially useful.
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23
ISSN:	0885-6125 1573-0565
DOI:	10.1007/s10994-013-5431-y