Robust Covariance Estimators Based on Information Divergences and Riemannian Manifold

This paper proposes a class of covariance estimators based on information divergences in heterogeneous environments. In particular, the problem of covariance estimation is reformulated on the Riemannian manifold of Hermitian positive-definite (HPD) matrices. The means associated with information div...

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Main Authors:	Xiaoqiang Hua, Yongqiang Cheng, Hongqiang Wang, Yuliang Qin
Format:	Article
Language:	English
Published:	MDPI AG 2018-03-01
Series:	Entropy
Subjects:	information divergence Riemannian manifold covariance estimation mean estimator heterogeneous clutter
Online Access:	http://www.mdpi.com/1099-4300/20/4/219

id	doaj-c9c8030879fb4d7da9dcae24b4c837f6
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spelling	doaj-c9c8030879fb4d7da9dcae24b4c837f62020-11-24T21:28:37ZengMDPI AGEntropy1099-43002018-03-0120421910.3390/e20040219e20040219Robust Covariance Estimators Based on Information Divergences and Riemannian ManifoldXiaoqiang Hua0Yongqiang Cheng1Hongqiang Wang2Yuliang Qin3School of Electronic Science, National University of Defence Technology, Changsha 410073, ChinaSchool of Electronic Science, National University of Defence Technology, Changsha 410073, ChinaSchool of Electronic Science, National University of Defence Technology, Changsha 410073, ChinaSchool of Electronic Science, National University of Defence Technology, Changsha 410073, ChinaThis paper proposes a class of covariance estimators based on information divergences in heterogeneous environments. In particular, the problem of covariance estimation is reformulated on the Riemannian manifold of Hermitian positive-definite (HPD) matrices. The means associated with information divergences are derived and used as the estimators. Without resorting to the complete knowledge of the probability distribution of the sample data, the geometry of the Riemannian manifold of HPD matrices is considered in mean estimators. Moreover, the robustness of mean estimators is analyzed using the influence function. Simulation results indicate the robustness and superiority of an adaptive normalized matched filter with our proposed estimators compared with the existing alternatives.http://www.mdpi.com/1099-4300/20/4/219information divergenceRiemannian manifoldcovariance estimationmean estimatorheterogeneous clutter
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Xiaoqiang Hua Yongqiang Cheng Hongqiang Wang Yuliang Qin
spellingShingle	Xiaoqiang Hua Yongqiang Cheng Hongqiang Wang Yuliang Qin Robust Covariance Estimators Based on Information Divergences and Riemannian Manifold Entropy information divergence Riemannian manifold covariance estimation mean estimator heterogeneous clutter
author_facet	Xiaoqiang Hua Yongqiang Cheng Hongqiang Wang Yuliang Qin
author_sort	Xiaoqiang Hua
title	Robust Covariance Estimators Based on Information Divergences and Riemannian Manifold
title_short	Robust Covariance Estimators Based on Information Divergences and Riemannian Manifold
title_full	Robust Covariance Estimators Based on Information Divergences and Riemannian Manifold
title_fullStr	Robust Covariance Estimators Based on Information Divergences and Riemannian Manifold
title_full_unstemmed	Robust Covariance Estimators Based on Information Divergences and Riemannian Manifold
title_sort	robust covariance estimators based on information divergences and riemannian manifold
publisher	MDPI AG
series	Entropy
issn	1099-4300
publishDate	2018-03-01
description	This paper proposes a class of covariance estimators based on information divergences in heterogeneous environments. In particular, the problem of covariance estimation is reformulated on the Riemannian manifold of Hermitian positive-definite (HPD) matrices. The means associated with information divergences are derived and used as the estimators. Without resorting to the complete knowledge of the probability distribution of the sample data, the geometry of the Riemannian manifold of HPD matrices is considered in mean estimators. Moreover, the robustness of mean estimators is analyzed using the influence function. Simulation results indicate the robustness and superiority of an adaptive normalized matched filter with our proposed estimators compared with the existing alternatives.
topic	information divergence Riemannian manifold covariance estimation mean estimator heterogeneous clutter
url	http://www.mdpi.com/1099-4300/20/4/219
work_keys_str_mv	AT xiaoqianghua robustcovarianceestimatorsbasedoninformationdivergencesandriemannianmanifold AT yongqiangcheng robustcovarianceestimatorsbasedoninformationdivergencesandriemannianmanifold AT hongqiangwang robustcovarianceestimatorsbasedoninformationdivergencesandriemannianmanifold AT yuliangqin robustcovarianceestimatorsbasedoninformationdivergencesandriemannianmanifold
_version_	1725969425618698240

Robust Covariance Estimators Based on Information Divergences and Riemannian Manifold

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