Orthogonal sparse eigenvectors: A procrustes problem

Konstantinos Benidis, Ying Sun, Prabhu Babu, Daniel P. Palomar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The problem of estimating sparse eigenvectors of a symmetric matrix attracts a lot of attention in many applications, especially those with high dimensional data set. While classical eigenvectors can be obtained as the solution of a maximization problem, existing approaches formulated this problem by adding a penalty term into the objective function that encourages a sparse solution. Nevertheless, the resulting methods achieve sparsity at a sacrifice of the orthogonality property. In this paper, we develop a new method to estimate dominant sparse eigenvectors without trading off their orthogonality. The problem is highly non-convex and too hard to handle. We apply the minorization-maximization (MM) framework where we iteratively maximize a tight lower bound (surrogate function) of the objective function over the Stiefel manifold. The inner maximization problem turns out to be the rectangular Procrustes problem, which has a closed-form solution. Numerical experiments show that the propose method matches or outperforms existing algorithms in terms of recovery probability and explained variance.

Original languageEnglish (US)
Title of host publication2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4683-4686
Number of pages4
ISBN (Electronic)9781479999880
DOIs
StatePublished - May 18 2016
Event41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Shanghai, China
Duration: Mar 20 2016Mar 25 2016

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2016-May
ISSN (Print)1520-6149

Conference

Conference41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016
CountryChina
CityShanghai
Period3/20/163/25/16

All Science Journal Classification (ASJC) codes

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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