TY - GEN
T1 - Group symmetry and non-Gaussian covariance estimation
AU - Soloveychik, Ilya
AU - Wiesel, Ami
PY - 2013
Y1 - 2013
N2 - We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler's scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization problems. Recently, it was shown that the underlying principle behind their success is an extended form of convexity over the geodesics in the manifold of positive definite matrices. A modern approach to improve estimation accuracy is to exploit prior knowledge via additional constraints, e.g., restricting the attention to specific classes of covariances which adhere to prior symmetry structures. In this paper, we prove that such group symmetry constraints are also geodesically convex and can therefore be incorporated into various non-Gaussian covariance estimators. Practical examples of such sets include: circulant, persymmetric and complex/quaternion proper structures. We provide a simple numerical technique for finding maximum likelihood estimates under such constraints, and demonstrate their performance advantage using synthetic experiments.
AB - We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler's scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization problems. Recently, it was shown that the underlying principle behind their success is an extended form of convexity over the geodesics in the manifold of positive definite matrices. A modern approach to improve estimation accuracy is to exploit prior knowledge via additional constraints, e.g., restricting the attention to specific classes of covariances which adhere to prior symmetry structures. In this paper, we prove that such group symmetry constraints are also geodesically convex and can therefore be incorporated into various non-Gaussian covariance estimators. Practical examples of such sets include: circulant, persymmetric and complex/quaternion proper structures. We provide a simple numerical technique for finding maximum likelihood estimates under such constraints, and demonstrate their performance advantage using synthetic experiments.
KW - Geodesic convexity
KW - Non-Gaussian covariance estimation
UR - http://www.scopus.com/inward/record.url?scp=84897695323&partnerID=8YFLogxK
U2 - 10.1109/GlobalSIP.2013.6737087
DO - 10.1109/GlobalSIP.2013.6737087
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AN - SCOPUS:84897695323
SN - 9781479902484
T3 - 2013 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2013 - Proceedings
SP - 1105
EP - 1108
BT - 2013 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2013 - Proceedings
T2 - 2013 1st IEEE Global Conference on Signal and Information Processing, GlobalSIP 2013
Y2 - 3 December 2013 through 5 December 2013
ER -