Various Types of Objective-Based Rough Clustering

Abstract

Conventional clustering algorithms classify a set of objects into some clusters with clear boundaries, that is, one object must belong to one cluster. However, many objects belong to more than one cluster in real world since the boundaries of clusters generally overlap with each other. Fuzzy set representation of clusters makes it possible for each object to belong to more than one cluster. On the other hand, it is pointed out that the fuzzy degree is sometimes regarded as too descriptive for interpreting clustering results. Instead of fuzzy representation, rough set one could deal with such cases. Clustering based on rough set could provide a solution that is less restrictive than conventional clustering and less descriptive than fuzzy clustering. Therefore, Lingras et al. (Lingras and Peters, Wiley Interdiscip Rev: Data Min Knowl Discov 1(1):64–72, 1207–1216, 2011, [1] and Lingras and West, J Intell Inf Syst 23(1):5–16, 2004, [2]) proposed a clustering method based on rough set, rough K-means (RKM). RKM is almost only one algorithm inspired by KM and some assumptions of RKM are very natural, however it is not useful from the viewpoint that the algorithm is not based on any objective functions. Outputs of non-hierarchical clustering algorithms strongly depend on initial values and the “better” output among many outputs from different initial values should be chosen by comparing the value of the objective function of the output with each other. Therefore the objective function plays very important role in clustering algorithms. From the standpoint, we have proposed some rough clustering algorithms based on objective functions. This paper shows such rough clustering algorithms which is based on optimization of an objective function.