E-function for Fuzzy Clustering in Complex Networks

Abstract

In many real-life situations, data consists of entities and the connections between them, which are naturally described by a complex network (graph). The structure of the network is often such that it is possible to group nodes based on the existence of connections between them, where such groups are called clusters (communities, modules). If the nodes are allowed to partially belong to clusters, they are called fuzzy (overlapping) clusters. There is a huge number of algorithms in the literature that perform fuzzy clustering, so a mechanism is needed to evaluate such clustering. The function that assesses the quality of a performed clustering is called the cluster quality function. One of the latest proposed quality functions is the E-function. The E-function is based on a comparison of the internal structure of a cluster, i.e., the connection between nodes within a cluster and the connection of its nodes with the nodes of other clusters. Due to its exponential nature, the E-function is sensitive to small changes in the membership degrees to which the nodes belong to clusters. As such, it has shown good results in evaluating clustering on known data sets. In this paper, the experimental results that the modified E-function achieves in the case of overlapping clusters are presented. Also, some possibilities for fuzzy clustering by optimizing the E-function are displayed.