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Orthogonal Sparse Eigenvectors: A Procrustes Problem

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.

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Paper Details

Authors:
Konstantinos Benidis, Ying Sun, Prabhu Babu, Daniel P. Palomar
Submitted On:
22 March 2016 - 2:22am
Short Link:
Type:
Poster
Event:
Presenter's Name:
Konstantinos Benidis
Paper Code:
3105
Document Year:
2016
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[1] Konstantinos Benidis, Ying Sun, Prabhu Babu, Daniel P. Palomar, "Orthogonal Sparse Eigenvectors: A Procrustes Problem", IEEE SigPort, 2016. [Online]. Available: http://sigport.org/954. Accessed: Aug. 24, 2019.
@article{954-16,
url = {http://sigport.org/954},
author = {Konstantinos Benidis; Ying Sun; Prabhu Babu; Daniel P. Palomar },
publisher = {IEEE SigPort},
title = {Orthogonal Sparse Eigenvectors: A Procrustes Problem},
year = {2016} }
TY - EJOUR
T1 - Orthogonal Sparse Eigenvectors: A Procrustes Problem
AU - Konstantinos Benidis; Ying Sun; Prabhu Babu; Daniel P. Palomar
PY - 2016
PB - IEEE SigPort
UR - http://sigport.org/954
ER -
Konstantinos Benidis, Ying Sun, Prabhu Babu, Daniel P. Palomar. (2016). Orthogonal Sparse Eigenvectors: A Procrustes Problem. IEEE SigPort. http://sigport.org/954
Konstantinos Benidis, Ying Sun, Prabhu Babu, Daniel P. Palomar, 2016. Orthogonal Sparse Eigenvectors: A Procrustes Problem. Available at: http://sigport.org/954.
Konstantinos Benidis, Ying Sun, Prabhu Babu, Daniel P. Palomar. (2016). "Orthogonal Sparse Eigenvectors: A Procrustes Problem." Web.
1. Konstantinos Benidis, Ying Sun, Prabhu Babu, Daniel P. Palomar. Orthogonal Sparse Eigenvectors: A Procrustes Problem [Internet]. IEEE SigPort; 2016. Available from : http://sigport.org/954