A New MCA-Based Divisive Hierarchical Algorithm for Clustering Categorical Data

Clustering categorical data faces two challenges, one is lacking of inherent similarity measure, and the other is that the clusters are prone to being embedded in different subspace. In this paper, we propose the first divisive hierarchical clustering algorithm for categorical data. The algorithm, which is based on multiple correspondence analysis (MCA), is systematic, efficient and effective. In our algorithm, MCA plays an important role in analyzing the data globally. The proposed algorithm has five merits. First, our algorithm yields a dendrogram representing nested groupings of patterns and similarity levels at different granularities. Second, it is parameter-free, fully automatic and, most importantly, requires no assumption regarding the number of clusters. Third, it is independent of the order in which the data are processed. Forth, it is scalable to large data sets; and finally, using the novel data representation and Chi-square distance measures makes our algorithm capable of seamlessly discovering the clusters embedded in the subspaces. Experiments on both synthetic and real data demonstrate the superior performance of our algorithm.