In this paper, we study the k-support norm regularized matrix pursuit problem, which is regarded as the core formulation for several popular computer vision tasks. The k-support matrix norm, a convex relaxation of the matrix sparsity combined with the ℓ2-norm penalty, generalizes the recently proposed k-support vector norm. The contributions of this work are two-fold. First, the proposed k-support matrix norm does not suffer from the disadvantages of existing matrix norms towards sparsity and/or low-rankness: 1) too sparse/dense, and/or 2) column independent. Second, we present an efficient procedure for k-support norm optimization, in which the computation of the key proximity operator is substantially accelerated by binary search. Extensive experiments on subspace segmentation, semi-supervised classification and sparse coding well demonstrate the superiority of the new regularizer over existing matrix-norm regularizers, and also the orders-of-magnitude speedup compared with the existing optimization procedure for the k-support norm. © 2014 Springer International Publishing.
CITATION STYLE
Lai, H., Pan, Y., Lu, C., Tang, Y., & Yan, S. (2014). Efficient k-support matrix pursuit. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8690 LNCS, pp. 617–631). Springer Verlag. https://doi.org/10.1007/978-3-319-10605-2_40
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