A min-max cut algorithm for graph partitioning and data clustering

An important application of graph partitioning is data clustering using a graph model - the pairwise similarities between all data objects form a weighted graph adjacency matrix that contains all necessary information for clustering. In this paper, we propose a new algorithm for graph partitioning with an objective function that follows the min-max clustering principle. The relaxed version of the optimization of the min-max cut objective function leads to the Fiedler vector in spectral graph partitioning. Theoretical analyses of min-max cut indicate that it leads to balanced partitions, and lower bounds are derived. The min-max cut algorithm is tested on newsgroup data sets and is found to out-perform other current popular partitioning/clustering methods. The linkage-based refinements to the algorithm further improve the quality of clustering substantially. We also demonstrate that a linearized search order based on linkage differential is better than that based on the Fiedler vector, providing another effective partitioning method.