Many-objective fuzzy centroids clustering algorithm for categorical data

Categorical data clustering algorithms, in contrast to numerical ones, are still in their infancy despite some algorithms have been proposed in the literature. It is known that many clustering algorithms are posed as optimization problems, where internal cluster validity functions are utilized as the objectives to find the optimal partitions. However, most of these methods consider a single criterion that can merely be applied to detect the particular structure/distribution of data. To overcome this issue, in this paper, a novel many objective fuzzy centroids clustering algorithms is proposed for categorical data using reference point based non-dominated sorting genetic algorithm, which simultaneously optimizes several cluster validity indices. In our work, an effective fuzzy centroids algorithm is employed to design the proposed approach, which is different from other contestant k-modes-type methods. Here, the fuzzy memberships are used for chromosome representation that combines with a novel genetic operation to produce new solutions. Moreover, a variable-length encoding scheme is developed for the sake of finding the clusters without knowing any prior knowledge. Experiments on several data sets demonstrate the superiority of the proposed algorithm over other state-of-the-art methods in terms of clustering accuracy and stability. On the other hand, our method can detect the cluster number if not predefined along with a desirable clustering solution.