The sparse matrix transform for covariance estimation and analysis of high dimensional signals
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, t...
| Veröffentlicht in: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. - 1992. - 20(2011), 3 vom: 15. März, Seite 625-40 |
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| Weitere Verfasser: | , |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2011
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society |
| Schlagworte: | Journal Article Research Support, U.S. Gov't, Non-P.H.S. |
| Zusammenfassung: | 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 |
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| Beschreibung: | Date Completed 27.05.2011 Date Revised 17.02.2011 published: Print-Electronic Citation Status MEDLINE |
| ISSN: | 1941-0042 |
| DOI: | 10.1109/TIP.2010.2071390 |