Elastic-Net Regularization of Singular Values for Robust Subspace Learning

Eunwoo Kim, Minsik Lee, Songhwai Oh; The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2015, pp. 915-923

Abstract


Learning a low-dimensional structure plays an important role in computer vision. Recently, a new family of methods, such as l1 minimization and robust principal component analysis, has been proposed for low-rank matrix approximation problems and shown to be robust against outliers and missing data. But these methods often require heavy computational load and can fail to find a solution when highly corrupted data are presented. In this paper, an elastic-net regularization based low-rank matrix factorization method for subspace learning is proposed. The proposed method finds a robust solution efficiently by enforcing a strong convex constraint to improve the algorithm's stability while maintaining the low-rank property of the solution. It is shown that any stationary point of the proposed algorithm satisfies the Karush-Kuhn-Tucker optimality conditions. The proposed method is applied to a number of low-rank matrix approximation problems to demonstrate its efficiency in the presence of heavy corruptions and to show its effectiveness and robustness compared to the existing methods.

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[bibtex]
@InProceedings{Kim_2015_CVPR,
author = {Kim, Eunwoo and Lee, Minsik and Oh, Songhwai},
title = {Elastic-Net Regularization of Singular Values for Robust Subspace Learning},
booktitle = {The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {June},
year = {2015}
}