Graph theoretic methods for clustering based on adjacency matrix and their comparison

Abstract

In this paper, we introduce a simple and new idea of link partition algorithm, direct line graph partition(DLP), using line graph transformation and traditional partition method. Two well-known algorithms, CPM(Clique Percolation method) and link clustering(LC) method, are introduced and compared to DLP. Since a usual line graph has more edges and nodes than its original graph, we selected faster partition algorithms, Fastgreedy and Walktrap, for line-graph partition. To compare goodness of algorithms, we adopt Mov. DLP is faster than CPM and shows better goodness of overlapping clustering. Concept of pair-wise link similarity is also applied to improve goodness of DLP. However, WDLP takes more time than DLP and shows almost same Mov. Briey speaking, there`s no considerable improvement goodness. In addition, we propose an algorithm, Finding-Local-Optimum (FLO), that finds a clustering with a local optimum when an objective function is given. We have conducted a set of experiments on networks. The result shows that methods based on WDLP and DLP with FLO produces a higher accuracy compared to LC. It`s complexity is smaller than CPM. Since CPM`s definition is too strict, it rarely returns overlapping clusters which covers all nodes in network. If one wants to do overlapping clustering with every node in a given network, DLP and WDLP can be good candidates for this.