Elastic-net regularization of singular values for robust subspace learning

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.