Fuzzy Graph Clustering based on Non-Euclidean Relational Fuzzy c-Means

Abstract

Graph clustering is a very popular research field with numerous practical applications. Here we focus on finding fuzzy clusters of nodes in unweighted, undirected, and irreflexive graphs. We introduce three new algorithms for fuzzy graph clustering (Newman-Girvan NERFCM, Small World NER-FCM, Signal NERFCM). Each of these three new algorithms uses a popular algorithm for crisp graph clustering and combines it with non-Euclidean rela-tional fuzzy c-means clustering (NERFCM). Experiments with artificial and real world data indicate that all three proposed algorithms perform quite well for compact clusters. For less compact clusters, Newman-Girvan NERFCM and Signal NERFCM also perform well. Newman-Girvan NERFCM is more robust to cluster overlaps, and Signal NER-FCM yields very smooth membership transitions.