Categorical-and-numerical-attribute data clustering based on a unified similarity metric without knowing cluster number

Most of the existing clustering approaches are applicable to purely numerical or categorical data only, but not the both. In general, it is a nontrivial task to perform clustering on mixed data composed of numerical and categorical attributes because there exists an awkward gap between the similarity metrics for categorical and numerical data. This paper therefore presents a general clustering framework based on the concept of object-cluster similarity and gives a unified similarity metric which can be simply applied to the data with categorical, numerical, and mixed attributes. Accordingly, an iterative clustering algorithm is developed, whose outstanding performance is experimentally demonstrated on different benchmark data sets. Moreover, to circumvent the difficult selection problem of cluster number, we further develop a penalized competitive learning algorithm within the proposed clustering framework. The embedded competition and penalization mechanisms enable this improved algorithm to determine the number of clusters automatically by gradually eliminating the redundant clusters. The experimental results show the efficacy of the proposed approach.