Clustering Categorical Data Using an Extended Modularity Measure

Newman and Girvan [12] recently proposed an objective function for graph clustering called the Modularity function which allows automatic selection of the number of clusters. Empirically, higher values of the Modularity function have been shown to correlate well with good graph clustering. In this paper we propose an extended Modularity measure for categorical data clustering; first, we establish the connection with the Relational Analysis criterion. The proposed Modularity measure introduces an automatic weighting scheme which takes in consideration the profile of each data object. A modified Relational Analysis algorithm is then presented to search for the partitions maximizing the criterion. This algorithm deals linearly with large data set and allows natural clusters identification, i.e. doesn’t require fixing the number of clusters and size of each cluster. Experimental results indicate that the new algorithm is efficient and effective at finding both good clustering and the appropriate number of clusters across a variety of real-world data sets.