文件名称：Covariance Estimation for High Dimensional Data Vectors Using the Sparse Matrix Transform
文件大小：507KB
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更新时间：2012-01-06 16:51:12
Covariance estimation
Covariance estimation for high dimensional vectors is a classically difcult 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 specically, 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 efciently estimated using greedy minimization of the log likelihood function, and the number of Givens rotations can be efciently computed using a cross-validation procedure. The resulting estimator is positive denite 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 proposed graphical lasso estimates for a variety of different classes and sample sizes.