Theoretical analysis of picture fuzzy clustering

Abstract

Recently, picture fuzzy clustering (FC-PFS) has been introduced as a new computational intelligence tool for various problems in knowledge discovery and pattern recognition. However, an important question that was lacked in the related researches in examination of mathematical properties behind the picture fuzzy clustering algorithm such as the convergence, the boundary or the convergence rate, etc. In this paper, we will prove that FC-PFS converges to at least one local minimum. Analysis on the loss function is also considered.