Supplementary materials to “Projective dictionary pair learning for pattern classification”

Shuhang Gu, Lei Zhang, Wangmeng Zuo, and Xiangchu Feng. “Supplementary materials to ‘Projective dictionary pair learning for pattern classification’.” Neural Information Processing Systems (2014).


In this file, we provide a detailed convergence analysis for the proposed DPL algorithm. We first introduce some related definitions of the bi-convex optimization problem [1, 2], and present the conclusions of the convergence of the alternative convex search (ACS) algorithm [3]. Then, we analyze the bi-convex property of our objective function, and show the equivalence between the ACS algorithm and our optimization algorithm.

1 Bi-convex problem and alternative convex search algorithm

We first introduce the basic definitions of bi-convex optimization problem, and then introduce the ACS algorithm used to solve it. The convergence of the ACS algorithm has been analyzed in [2].

Definition 1.

2 Convergence analysis of DPL