JLMC: A clustering method based on Jordan-Form of Laplacian-Matrix

Abstract

Among the current clustering algorithms of complex networks, Laplacian-based spectral clustering algorithms have the advantage of rigorous mathematical basis and high accuracy. However, their applications are limited due to their dependence on prior knowledge, such as the number of clusters. For most of application scenarios, it is hard to obtain the number of clusters beforehand. To address this problem, we propose a novel clustering algorithm - Jordan-Form of Laplacian-Matrix based Clustering algorithm (JLMC). In JLMC, we propose a model to calculate the number (n) of clusters in a complex network based on the Jordan-Form of its corresponding Laplacian matrix. JLMC clusters the network into n clusters by using our proposed modularity density function (P function). We conduct extensive experiments over real and synthetic data, and the experimental results reveal that JLMC can accurately obtain the number of clusters in a complex network, and outperforms Fast-Newman algorithm and Girvan-Newman algorithm in terms of clustering accuracy and time complexity.