Definition and Goal of Graph Clustering -Motivation to Explore a New Algorithm

Abstract

In recent years, one of the popular method for mining evolving data, is to convert it to a network, in fact an adjacency matrix, where data units are nodes and their relations/similarity are the link weights. The network is then partitioned into communities to explore information hidden in the data. For last 50 years, various graph partitioning algorithms are proposed. Depending on the application, the optimization objective of the partitioning and the resulting clusters are different. Different algorithms, based on Linear Algebra, heuristics with different greedy optimization criterion, agglomerative algorithms, are proposed to meet different optimization criterion suitable for target network and application.In this work we proposed a genetic algorithm (GA) based dynamic clustering algorithm. Genetic algorithm (GA) for graph clustering, with fitness function as the modularity index, is already proposed, in our previous works. In this work, we propose a multimodal GA. The algorithm starts with modularity index (Q) as the optimization criterion. Once converged, we add another term in the fitness function which will balance the cardinalities of the partitions. The parameters are computed based on the partitions after the first stage of convergence. We continue to run the Genetic search with modified fitness function until a second convergence is achieved. In all our experiments, not only could we achieve better balance of the size of different clusters, in many experiments it actually improved the modularity index. For a highly modular graph, with Q ≥ 0.7, most of the algorithms produce the same result. When the optimum modularity index of the graph is low, GA with only modularity index as optimization criterion usually converges in local minimum. With the proposed modification, we could always find clustering with an improved Q value. We run popular partitioning algorithms on known real-world networks and found that the proposed algorithm could find better partitioning, closest to reality.