Categorical data clustering with automatic selection of cluster number

In this paper, we investigate the problem of determining the number of clusters in the k-modes based categorical data clustering process. We propose a new categorical data clustering algorithm with automatic selection of k. The new algorithm extends the k-modes clustering algorithm by introducing a penalty term to the objective function to make more clusters compete for objects. In the new objective function, we employ a regularization parameter to control the number of clusters in a clustering process. Instead of finding k directly, we choose a suitable value of regularization parameter such that the corresponding clustering result is the most stable one among all the generated clustering results. Experimental results on synthetic data sets and the real data sets are used to demonstrate the effectiveness of the proposed algorithm.