Categorical data clustering: What similarity measure to recommend?

Inside the clustering problem of categorical data resides the challenge of choosing the most adequate similarity measure. The existing literature presents several similarity measures, starting from the ones based on simple matching up to the most complex ones based on Entropy. The following issue, therefore, is raised: is there a similarity measure containing characteristics which offer more stability and also provides satisfactory results in databases involving categorical variables? To answer this, this work compared nine different similarity measures using the TaxMap clustering mechanism, and in order to evaluate the clustering, four quality measures were considered: NCC, Entropy, Compactness and Silhouette Index. Tests were performed in 15 different databases containing categorical data extracted from public repositories of distinct sizes and contexts. Analyzing the results from the tests, and by means of a pairwise ranking, it was observed that the coefficient of Gower, the simplest similarity measure presented in this work, obtained the best performance overall. It was considered the ideal measure since it provided satisfactory results for the databases considered.