Efficient k-Support Matrix Pursuit

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 ℓ

2

-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.