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2008

Covariance Estimation for High Dimensional Data Vectors Using the Sparse Matrix Transform

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Covariance Estimation for High Dimensional Data Vectors Using the Sparse Matrix Transform
Covariance estimation for high dimensional vectors is a classically difficult problem in statistical analysis and machine learning. In this paper, we propose a maximum likelihood (ML) approach to covariance estimation, which employs a novel sparsity constraint. More specifically, the covariance is constrained to have an eigen decomposition which can be represented as a sparse matrix transform (SMT). The SMT is formed by a product of pairwise coordinate rotations known as Givens rotations. Using this framework, the covariance can be efficiently estimated using greedy minimization of the log likelihood function, and the number of Givens rotations can be efficiently computed using a cross-validation procedure. The resulting estimator is positive definite and well-conditioned even when the sample size is limited. Experiments on standard hyperspectral data sets show that the SMT covariance estimate is consistently more accurate than both traditional shrinkage estimates and recently propose...
Guangzhi Cao, Charles A. Bouman
Added 29 Oct 2010
Updated 29 Oct 2010
Type Conference
Year 2008
Where NIPS
Authors Guangzhi Cao, Charles A. Bouman
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