Categorical fuzzy entropy c-means

Hard and fuzzy clustering algorithms are part of the partition-based clustering family. They are widely used in real-world applications to cluster numerical and categorical data. While in hard clustering an object is assigned to a cluster with certainty, in fuzzy clustering an object can be assigned to different clusters given a membership degree. For both types of method an entropy can be incorporated into the objective function, mostly to avoid solutions raising too much uncertainties. In this paper, we present an extension of a fuzzy clustering method for categorical data using fuzzy centroids. The new algorithm, referred to as Categorical Fuzzy Entropy (CFE), integrates an entropy term in the objective function. This allows a better fuzzification of the cluster prototypes. Experiments on ten real-world data sets and statistical comparisons show that the new method can efficiently handle categorical data.