Clustering categorical data via Hamming distance

Clustering methods have typically found their application when dealing with continuous data. However, in many modern applications data consist of multiple categorical variables with no natural ordering. In the heuristic framework the problem of clustering these data is tackled by introducing suitable distances. In this work, we develop a model-based approach for clustering categorical data with nominal scale. Our approach is based on a mixture of distributions defined via the Hamming distance between categorical vectors. Maximum likelihood inference is delivered through an expectation-maximization algorithm. A simulation study is carried out to illustrate the proposed approach.