IEEE Trans Image Process - The sparse matrix transform for covariance estimation and analysis of high dimensional signals.

Tópicos

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Resumo

Covariance estimation for high dimensional signals is a classically difficult problem in statistical signal analysis and machine learning. In this paper, we propose a maximum likelihood (ML) approach to covariance estimation, which employs a novel non-linear 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 optimization of the log-likelihood function, and the number of Givens rotations can be efficiently computed using a cross-validation procedure. The resulting estimator is generally positive definite and well-conditioned, even when the sample size is limited. Experiments on a combination of simulated data, standard hyperspectral data, and face image sets show that the SMT-based covariance estimates are consistently more accurate than both traditional shrinkage estimates and recently proposed graphical lasso estimates for a variety of different classes and sample sizes. An important property of the new covariance estimate is that it naturally yields a fast implementation of the estimated eigen-transformation using the SMT representation. In fact, the SMT can be viewed as a generalization of the classical fast Fourier transform (FFT) in that it uses "butterflies" to represent an orthonormal transform. However, unlike the FFT, the SMT can be used for fast eigen-signal analysis of general non-stationary signals.

Resumo Limpo

covari estim high dimension signal classic difficult problem statist signal analysi machin learn paper propos maximum likelihood ml approach covari estim employ novel nonlinear sparsiti constraint specif covari constrain eigen decomposit can repres spars matrix transform smt smt form product pairwis coordin rotat known given rotat use framework covari can effici estim use greedi optim loglikelihood function number given rotat can effici comput use crossvalid procedur result estim general posit definit wellcondit even sampl size limit experi combin simul data standard hyperspectr data face imag set show smtbase covari estim consist accur tradit shrinkag estim recent propos graphic lasso estim varieti differ class sampl size import properti new covari estim natur yield fast implement estim eigentransform use smt represent fact smt can view general classic fast fourier transform fft use butterfli repres orthonorm transform howev unlik fft smt can use fast eigensign analysi general nonstationari signal

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