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Covariance matrix estimation with multi-regularization parameters based on MDL principle
Zhou X.1; Guo P.1; Chen C.L.P.2
2013
Source PublicationNeural Processing Letters
ISSN13704621 1573773X
Volume38Issue:2Pages:227-238
AbstractRegularization is a solution for the problem of unstable estimation of covariance matrix with a small sample set in Gaussian classifier. In many applications such as image restoration, sparse representation, we have to deal with multi-regularization parameters problem. In this paper, the case of covariance matrix estimation with multi-regularization parameters is investigated, and an estimate method called as KLIM-L is derived theoretically based on Minimum Description Length (MDL) principle for the small sample size problem with high dimension setting. KLIM-L estimator can be regarded as a generalization of KLIM estimator in which local difference in each dimension is considered. Under the framework of MDL principle, a selection method of multi-regularization parameters is also developed based on the minimization of the Kullback-Leibler information measure, which is simply and directly estimated by point estimation under the approximation of two-order Taylor expansion. The computational cost to estimate multi-regularization parameters with KLIM-L method is less than those with RDA (Regularized Discriminant Analysis) and LOOC (leave-one-out covariance matrix estimate) in which cross validation technique is adopted. Experiments show that higher classification accuracy can be achieved by using the proposed KLIM-L estimator. © 2012 Springer Science+Business Media New York.
KeywordCovariance matrix estimation Gaussian classifier Minimum description length Principle Multi-regularization parameters selection
DOI10.1007/s11063-012-9272-7
URLView the original
Language英語
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Cited Times [WOS]:3   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF COMPUTER AND INFORMATION SCIENCE
Affiliation1.Beijing Normal University
2.Universidade de Macau
3.Beijing City University
Recommended Citation
GB/T 7714
Zhou X.,Guo P.,Chen C.L.P.. Covariance matrix estimation with multi-regularization parameters based on MDL principle[J]. Neural Processing Letters,2013,38(2):227-238.
APA Zhou X.,Guo P.,&Chen C.L.P..(2013).Covariance matrix estimation with multi-regularization parameters based on MDL principle.Neural Processing Letters,38(2),227-238.
MLA Zhou X.,et al."Covariance matrix estimation with multi-regularization parameters based on MDL principle".Neural Processing Letters 38.2(2013):227-238.
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