A novel automatic picture fuzzy clustering method based on particle swarm optimization and picture composite cardinality

Fuzzy clustering plays an important role in pattern recognition and knowledge discovery. Recently, there has been a great interest of developing fuzzy clustering algorithms on advanced fuzzy sets such as Picture Fuzzy Clustering (FC-PFS) which is an extension of Fuzzy C-Means on Picture Fuzzy Set. A major disadvantage of FC-PFS is how to define a prior number of clusters before clustering. Because each dataset has distinctive features and distributions of patterns, determining such the number for a clustering algorithm would result in good quality. In this paper, we propose a method called Automatic Picture Fuzzy Clustering (AFC-PFS) for determining the most suitable number of clusters for FC-PFS. It is a hybrid method between Particle Swarm Optimization (PSO) and FC-PFS where combined solutions consisting of the number of clusters and equivalent clustering centers and membership matrices are packed and optimized in PSO. A new term namely Picture Composite Cardinality is also given to determine a suitable number of clusters. AFC-PFS is empirically validated on benchmark datasets of UCI Machine Learning Repository by different clustering quality indices. The results show that AFC-PFS has better performance than the relevant methods.