Weighted Laplacian Method and Its Theoretical Applications

Abstract

Recently, a class of multilevel graph clustering (graph partitioning) algorithms have been extensively studied due to their practical utility. Although these newly proposed algorithms work well, there is still not many theoretical guarantees for the quality of partition in these existing methods due to their intrinsic heuristic properties to a great extent. In this paper, we propose a novel weighted Laplacian method for the multilevel graph clustering problem with more powerful theoretical background to further improve clustering performance mainly in terms of accuracy. Since our algorithm inherits the virtues of spectral methods, it possesses a friendly optimization property since it can produce the global optimal solution of a relaxation to the weighted cut on the coarsened graph in the middle stage. Meanwhile, the multilevel strategy can make it possible for our method to produce final clustering results with reasonable time range. Additionally, the weighted graph Laplacian is also suitable for doubly-weighted graph, which will endow our algorithm with a potential wide range of applications. The experimental results verify that our weighted Laplacian methods is indeed superior over existing algorithms in terms of clustering accuracy while also maintains comparable clustering speed.