By Topic

A Bayesian approach to geometric subspace estimation

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Srivastava, A. ; Dept. of Stat., Florida State Univ., Tallahassee, FL, USA

This paper presents a geometric approach to estimating subspaces as elements of the complex Grassmann-manifold, with each subspace represented by its unique, complex projection matrix. Variation between the subspaces is modeled by rotating their projection matrices via the action of unitary matrices [elements of the unitary group U(n)]. Subspace estimation or tracking then corresponds to inferences on U(n). Taking a Bayesian approach, a posterior density is derived on U(n), and certain expectations under this posterior are empirically generated. For the choice of the Hilbert-Schmidt norm on U(n), to define estimation errors, an optimal MMSE estimator is derived. It is shown that this estimator achieves a lower bound on the expected squared errors associated with all possible estimators. The estimator and the bound are computed using (Metropolis-adjusted) Langevin's-diffusion algorithm for sampling from the posterior. For use in subspace tracking, a prior model on subspace rotation, that utilizes Newtonian dynamics, is suggested

Published in:

Signal Processing, IEEE Transactions on  (Volume:48 ,  Issue: 5 )