Characterizing the fuzzy community structure in link graph via the likelihood optimization

Abstract

Detecting fuzzy communities in networks is a critical but challenging task in many fields including biology, technology, social system and so on. Current technology is largely reliant on network topology, which can’t provide much useful information such module correlations and hierarchies. This paper introduces a new fuzzy community detection method by maximizing the likelihood function, which can dynamically map the link community structure to the optimal state. To specify the direction and weight of the link graph, the directional node graph is first converted into a new type of link graph. Next, we define a communityunit consisting of membership and correlation information in a link graph. Specially, we define this likelihood function with a posteriori probability that aims to find the optimal partition under the prior conditions of given link graph and granularity. Furthermore, based on the spectral analysis of Markov transition matrices, we give a strict mathematical analysis for identifying the optimal number of network communities by analyzing the stability of community structures. Finally, extensive experiments on both artificial benchmarks and real-world networks show that our algorithm consistently achieving higher accuracy than classical methods.