Three Fuzzy Clustering Algorithms for Nominal Data: Enhancement Through Tsallis Entropy-Based Feature Weighting and Q-Divergence-Based Fuzzification

Among many clustering algorithms, the dissimilarity between an object and a cluster center is measured using the inner-product-induced squared distance. Such a measure cannot be used for nominal data, that is, a type of data to label the variables without providing any quantitative values. This study proposed three fuzzy clustering algorithms for nominal data. Each algorithm was constructed using three distinct conventional algorithms via parameter extension in a manner similar to how the Shannon entropy was extended to the Tsallis entropy and the Kullback-Leibler divergence was extended to q-divergence using other parameters. The theoretical results indicated that the proposed algorithms extended the basis in terms of problem setting. The results of numerical experiments using real datasets demonstrated that the proposed algorithms outperformed their basis in terms of the clustering accuracy.