Optimizing kernel possibilistic fuzzy C-means clustering using metaheuristic algorithms

Over the past decade, metaheuristic algorithms have gained significant attention from researchers due to their effectiveness and computational efficiency. Conventional clustering algorithms often suffer from various limitations, but the use of metaheuristic algorithms into clustering has shown promising results in achieving globally optimal centroid positions within clusters. The paper shows the implementation of metaheuristic algorithms with the kernel possibilistic fuzzy c-means algorithm (KPFCM), leading to notable improvements under normal as well as under noisy conditions. Furthermore, this paper focuses on optimizing the objective functions (case-1: single objective function; case-2: multiobjective function) through the utilization of the kernel trick and the probabilistic nature of metaheuristic algorithms, specifically genetic algorithm (GA), particle swarm optimization (PSO), and teaching learning-based optimization (TLBO) algorithm. The proposed approach is evaluated on six benchmark datasets, considering both single objective function optimization (case-1) and multiobjective function optimization (case-2). In case-1, three hybrid algorithms are introduced for single objective function optimization: the genetic algorithm-based kernel possibilistic fuzzy c-means (GA-KPFCM) algorithm, the particle swarm optimization-based kernel possibilistic fuzzy c-means (PSO-KPFCM) algorithm, and the teaching learning-based optimization with kernel possibilistic fuzzy c-means (TLBO-KPFCM) algorithm. Results obtained from these algorithms demonstrate improved performance compared to traditional possibilistic fuzzy c-means (PFCM) and kernel possibilistic fuzzy c-means (KPFCM) algorithms. Additionally, a comparative analysis of hybrid metaheuristic with kernel possibilistic fuzzy c-means algorithms is conducted against hybrid metaheuristic fuzzy c-means algorithms and hybrid metaheuristic possibilistic fuzzy c-means algorithms, confirming the superiority of the proposed hybrid combinations. For multiobjective optimization (MOO) clustering, a Pareto front is established using the concept of non-dominated solutions. The proposed multiobjective hybrid algorithms (case-2) for optimization include the multiobjective particle swarm optimization kernel possibilistic fuzzy c-means (MPSO-KPFCM) algorithm, the non-dominated sorting genetic algorithm third generation kernel possibilistic fuzzy c-means (NSGAIII-KPFCM) algorithm, and the non-dominated sorting teaching learning-based optimization kernel possibilistic fuzzy c-means (NSTLBO-KPFCM) algorithm. These algorithms demonstrate their effectiveness in achieving optimal solutions for multiobjective clustering problems.