A Novel Multi-objective Approach to Fuzzy Clustering

A clustering algorithm is an unsupervised method, which aims to divide data points into two groups or more. These algorithms generally rely on the optimization of a single criterion to find optimal cluster structures. This choice might lead to cluster structures of poor quality, and does not reflect how humans generally rely on multiple (possibly conflicting) criteria when grouping similar elements together. In this paper, we apply an different approach based on multi-objective optimization to solve the problem of fuzzy clustering. Specifically, we combine the objective function of the popular fuzzy c-means algorithm with a second objective function, which aims at maximizing the number of data points having a high degree of membership to one of the clusters. The rationale is that data points close to a cluster center have a high membership value, while data points in between cluster centers share their membership between the different clusters: by optimizing the second criterion we expect an improvement of the quality of the resulting clustering structure. We perform the multi-objective optimization by means of the Non-dominated Sorting Genetic Algorithm (NSGA-II), a multi-objective, evolutionary global optimization algorithm. Our results show that a multi-objective approach to fuzzy clustering can generate solutions of higher quality than classic fuzzy C-means, on both synthetic and real world data sets.