From Soft Clustering to Hard Clustering: A Collaborative Annealing Fuzzy $c$-Means Algorithm

The fuzzy c-means clustering algorithm is the most widely used soft clustering algorithm. In contrast to hard clustering, the cluster membership of data generated using the fuzzy c-means algorithm is ambiguous. Similar to hard clustering algorithms, the clustering results of the fuzzy c-means clustering algorithm are also suboptimal with varied performance depending on initial solutions. In this paper, a collaborative annealing fuzzy c-means algorithm is presented. To address the issue of ambiguity, the proposed algorithm leverages an annealing procedure to phase out the fuzzy cluster membership degree toward a crispy one by reducing the exponent gradually according to a cooling schedule. To address the issue of suboptimality, the proposed algorithm employs multiple fuzzy c-means modules to generate alternative clusters based on memberships repeatedly reinitialized using a metaheuristic rule. Experimental results on eight benchmark datasets are elaborated to demonstrate the superiority of the proposed algorithm to thirteen prevailing hard and soft algorithms in terms of internal and external cluster validity indices.