NDLI: Minimum Mean Square Distance Estimation of a Subspace

Content Provider	IEEE Xplore Digital Library
Author	Besson, O. Dobigeon, N. Tourneret, J.-Y.
Copyright Year	1991
Abstract	We consider the problem of subspace estimation in a Bayesian setting. Since we are operating in the Grassmann manifold, the usual approach which consists of minimizing the mean square error (MSE) between the true subspace U and its estimate U may not be adequate as the MSE is not the natural metric in the Grassmann manifold G_N,p, i.e., the set of p-dimensional subspaces in R^N. As an alternative, we propose to carry out subspace estimation by minimizing the mean square distance between U and its estimate, where the considered distance is a natural metric in the Grassmann manifold, viz. the distance between the projection matrices. We show that the resulting estimator is no longer the posterior mean of U but entails computing the principal eigenvectors of the posterior mean of UU^T. Derivation of the minimum mean square distance (MMSD) estimator is carried out in a few illustrative examples including a linear Gaussian model for the data and Bingham or von Mises Fisher prior distributions for U. In all scenarios, posterior distributions are derived and the MMSD estimator is obtained either analytically or implemented via a Markov chain Monte Carlo simulation method. The method is shown to provide accurate estimates even when the number of samples is lower than the dimension of U. An application to hyperspectral imagery is Anally investigated.
Sponsorship	IEEE Signal Processing Society
Starting Page	5709
Ending Page	5720
Page Count	12
File Size	967553
File Format	PDF
ISSN	1053587X
Volume Number	59
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-12-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Mean square error methods Manifolds Bayesian methods Signal to noise ratio Covariance matrix Markov processes Monte Carlo methods subspace estimation Bayesian inference minimum mean-square distance (MMSD) estimation simulation method Stiefel manifold
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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