FKMAWCW: Categorical fuzzy k-modes clustering with automated attribute-weight and cluster-weight learning

The fuzzy k-modes (FKM) is a popular method for clustering categorical data. However, the main problem of this algorithm is that it is very sensitive to the initialization of primary clusters, so inappropriate initial cluster centers lead to poor local optima. Another problem with the FKM is the equal importance of the attributes used during the clustering process, which in real applications, the importance of the attributes are different, and some attributes are more important than others. Some versions of FKM have been presented in the literature, each of which has somehow solved one of the above problems. In this paper, we propose a new clustering method (FKMAWCW) to solve mentioned problems at the same time. In the proposed clustering process, a local attribute weighting mechanism is used to weight the attributes of each cluster properly. Also, a cluster weighting mechanism is proposed to solve the initialization sensitivity. Attribute weight and cluster weight are learned simultaneously and automatically during the clustering process. In addition, to reduce the noise sensitivity, a new distance function is proposed. So, the proposed algorithm can tolerate noisy environment. Extensive experiments on 11 benchmark datasets and an artificially generated dataset show that the proposed algorithm performs better than the state-of-the-art algorithms. This paper presents mathematical analyses to obtain updating functions, providing the convergence proof of the algorithm. The implementation source code of FKMAWCW is made publicly available at https://github.com/Amin-Golzari-Oskouei/FKMAWCW.