COVARIENCE ESTIMATION AND PERFORMANCE OF SATELLITE IMAGINARY DATA USING SMT
G Sri Harshini, Jampala Chaitanya · 2013
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 havean Eigen decomposition which can be represented as a sparse matrix transforms (SMT). The SMT is formed by a product of pairwise coordinate rotations knownas 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 whenthe sample size is limited. Experiments on standard hyper-spectral 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.