A Note on Fuzzy Even-Sized Noise Clustering

Abstract

Clustering is an unsupervised learning and can be broadly classified into hierarchical and non-hierarchical methods. Among non-hierarchical methods, those based on objective function optimization have been studied extensively from the viewpoint of not only effectiveness but also theoretical depth. Fuzzified Even-sized Clustering Based on Optimization (FECBO) is a method that focuses on clustering with the constraint that the cluster sizes are equal in terms of the fuzzy membership. However, FECBO has the problem of being susceptible to noise. To solve this problem, a method was proposed that introduces the idea of noise clustering into FECBO, called Fuzzy Even-sized Noise Clustering (FENC). Nevertheless, FENC consists of a noise clustering phase and a FECBO phase, each of which is run separately, which makes the algorithm more complex. Also, from the standpoint of run time, better results may be obtained if these two phases are performed at the same time. In this paper, we propose a simpler algorithm that combines these two phases. Furthermore, we attempt to introduce a kernel function to perform classification by nonlinear boundaries. We then compare the proposed method with conventional methods through numerical examples.