title: Uncovering and testing the fuzzy clusters based on lumped Markov chain in complex network.
abstract: Identifying clusters, namely groups of nodes with comparatively strong internal connectivity, is a fundamental task for deeply understanding the structure and function of a network. By means of a lumped Markov chain model of a random walker, we propose two novel ways of inferring the lumped markov transition matrix. Furthermore, some useful results are proposed based on the analysis of the properties of the lumped Markov process. To find the best partition of complex networks, a novel framework including two algorithms for network partition based on the optimal lumped Markovian dynamics is derived to solve this problem. The algorithms are constructed to minimize the objective function under this framework. It is demonstrated by the simulation experiments that our algorithms can efficiently determine the probabilities with which a node belongs to different clusters during the learning process and naturally supports the fuzzy partition. Moreover, they are successfully applied to real-world network, including the social interactions between members of a karate club.
authors.affiliation: University Key Laboratory of Wireless Sensor Networks in Yunnan Province, Yunnan University of Nationalities, Kunming, P.R. China.
authors.forename: Fan
authors.initials: F
authors.lastname: Jing
authors.affiliation: School of Urban Construction and Management, Yunnan University, Kunming, P.R. China.
authors.forename: Xie
authors.initials: X
authors.lastname: Jianbin
authors.affiliation: University Key Laboratory of Wireless Sensor Networks in Yunnan Province, Yunnan University of Nationalities, Kunming, P.R. China.
authors.forename: Wang
authors.initials: W
authors.lastname: Jinlong
authors.affiliation: University Key Laboratory of Wireless Sensor Networks in Yunnan Province, Yunnan University of Nationalities, Kunming, P.R. China.
authors.forename: Qu
authors.initials: Q
authors.lastname: Jinshuai
mesh_terms: D000465:Algorithms; D016000:Cluster Analysis; D017143:Fuzzy Logic; D006801:Humans; D008390:Markov Chains; D012944:Social Support; D013269:Stochastic Processes; D013598:Systems Theory