Graph K-means Based on Leader Identification, Dynamic Game, and Opinion Dynamics

Abstract

With the explosion of social media networks, many modern applications are concerning about people's connections, which leads to the so-called social computing. An elusive question is to study how opinion communities form and evolve in real-world networks with great individual diversity and complex human connections. In this scenario, the classic K-means technique and its extended versions could not be directly applied, as they largely ignore the relationship among interactive objects. On the other side, traditional community detection approaches in statistical physics would be neither adequate nor fair: they only consider the network topological structure but ignore the heterogeneous-objects' attributive information. To this end, we attempt to model a realistic social media network as a discrete-time dynamical system, where the opinion matrix and the community structure could mutually affect each other. In this paper, community detection in social media networks is naturally formulated as a multi-objective optimization problem (MOOP), i.e., finding a set of densely connected components with similar opinion vectors. We propose a novel and powerful graph K-means framework, which is composed of three coupled phases in each discrete-time period. Specifically, the first phase uses a fast heuristic approach to identify those opinion leaders who have relatively high local reputation; the second phase adopts a novel dynamic game model to find the locally Pareto-optimal community structure; and the final phase employs a robust opinion dynamics model to simulate the evolution of the opinion matrix. We conduct a series of comprehensive experiments on real-world benchmark networks to validate the performance of GK-means through comparisons with the state-of-the-art graph clustering technologies.