Local Graph Clustering Using l1-regularized PageRank Algorithms

Abstract

Local graph clustering methods are used to find small- and medium-scale clusters without traversing the graph. It has been shown that the combination of Approximate Personalized PageRank (APPR) algorithm and sweep method can efficiently detect a small cluster around the starting vertex. This research explores the optimization framework proposed in the work by Fountoulakis et al., where a connection between the APPR and an l1-regularized objective function is revealed. We propose a coordinate descent method for solving the l1-regularized PageRank problem. We prove that our method has running time dependent on the number of nonzero coordinates in the optimal solution. In addition, we compare 6 optimization algorithms for solving the l1-regularized PageRank problem in large graphs. We demonstrate that the proposed coordinate descent outperforms the original proximal gradient descent, and the accelerated first order algorithms have the best performance among all algorithms measured in our experiment.