A Fast Proximal Point Algorithm For Generalized Graph Laplacian Learning

Graph learning is one of the most important tasks in machine learning, statistics and signal processing. In this paper, we focus on the problem of learning the generalized graph Laplacian (GGL) and propose an efficient algorithm to solve it. We first fully exploit the sparsity structure hidden in the objective function by utilizing soft-thresholding technique to transform the GGL problem into an equivalent problem. Moreover, we propose a fast proximal point algorithm (PPA) to solve the transformed GGL problem and establish the linear convergence rate of our algorithm. Extensive numerical experiments on both synthetic data and real data demonstrate that the soft-thresholding technique accelerates our PPA method and PPA can outperform the current state-of-the-art method in terms of speed.