Experimental evaluation of Szemerédi’s regularity lemma in graph-based clustering

Abstract

One major problem of graph-based clustering lies in the large computation load resulted by the similarity graph. Several previous works have shown that Szemerédi’s regularity lemma can be useful in relieving this problem. Based on this lemma, we partition the original graph to obtain a reduced graph, which inherits the major structure of the original graph with a much smaller cardinality. By performing clustering on the reduced graph and mapping data labels back to the original graph, the computation load can be reduced significantly. In further works we found that the parameters of this method have significant influences on the clustering results, and this issue hasn’t been dealt with in previous works. In this paper we present a thorough investigation of the influences of the parameters on clustering results, in experiments with four representative algorithms and a large number of real datasets. As a result, we find out the appropriate ranges of parameters to improve both clustering accuracy and computation efficiency significantly. We also show that regularity partitioning outperforms ordinary k-means-based partitioning, demonstrating the advantage of the regularity lemma in building the reduced graph. Furthermore, experimental results show that relatively old algorithms can be enhanced based on this lemma to outperform recent state-of-the-art ones. This work goes a step further in extending the application of the regularity lemma from pure theoretical to practical realms.