Belief relational clustering and its application to community detection

Abstract : Communities are groups of nodes (vertices) which probably share common properties and/or play similar roles within the graph. They can extract specific structures from complex networks, and consequently community detection has attracted considerable attention crossing many areas where systems are often represented as graphs. We consider in this work to represent graphs as relational data, and propose models for the corresponding relational data clustering. Four approaches are brought forward to handle the community detection problem under different scenarios. We start with a basic situation where nodes in the graph are clustered based on the dissimilarities and propose a new c-partition clustering approach named Median Evidential C-Means (MECM) algorithm. This approach extends the median clustering methods in the framework of belief function theory. Moreover, a community detection scheme based on MECM is presented. The proposed approach could provide credal partitions for data sets with only known dissimilarities. The dissimilarity measure could be neither symmetric nor fulfilling any metric requirements. It is only required to be of intuitive meaning. Thus it expands application scope of credal partitions. In order to capture various aspects of the community structures, we may need more members rather than one to be referred as the prototypes of an individual group. Motivated by this idea, a Similarity-based Multiple Prototype (SMP) community detection approach is proposed. The centrality values are used as the criterion to select multiple prototypes to characterize each community. The prototype weights are derived to describe the degree of representativeness of objects for their own communities. Then the similarity between each node and community is defined, and the nodes are partitioned into divided communities according to these similarities. Crisp and fuzzy partitions could be obtained by the application of SMP. Following, we extend SMP in the framework of belief functions to get credal partitions so that we can gain a better understanding of the data structure. The prototype weights are incorporate into the objective function of evidential clustering. The mass membership and the prototype weights could be updated alternatively during the optimization process. In this case, each cluster could be described using multiple weighted prototypes. As we will show, the prototype weights could also provide us some useful information for structure analysis of the data sets. Lastly, the original update rule and propagation criterion of LPA are extended in the framework of belief functions. A new community detection approach, called Semi-supervised Evidential Label Propagation (SELP), is proposed as an enhanced version of the conventional LPA. One of the advantages of SELP is that it could take use of the available prior knowledge about the community labels of some individuals. This is very common in real practice. In SELP, the nodes are divided into two parts. One contains the labeled nodes, and the other includes the unlabeled ones. The community labels are propagated from the labeled nodes to the unlabeled ones step by step according to the proposed evidential label propagation rule. The performance of the proposed approaches is evaluated using benchmark graph data sets and generated graphs. Our experimental results illustrate the effectiveness of the proposed clustering algorithms and community detection approaches.
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Kuang Zhou. Belief relational clustering and its application to community detection. Probability [math.PR]. Université Rennes 1, 2016. English. ⟨NNT : 2016REN1S027⟩. ⟨tel-01395061⟩

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