On Some Models of Objective-Based Rough Clustering

Fuzzy clustering which can implement flexible classification is very useful but sometimes calculates the degrees of belongingness of an objects to a cluster too exactly. To solve this problem, a new clustering method called rough k-means (RKM) is proposed by Lingras et al. RKM which is an extended method by using rough set representation can classify more roughly than fuzzy clustering without lack of flexibility. Generally, non-hierarchical clustering methods including RKM are strongly dependent on initial values. Therefore we need some indicator to evaluate outputs of a method. Many methods define an objective function as the indicator. However conventional rough clustering methods including RKM are not based on an objective function. Thus we cannot evaluate the outputs of them. We solve this problem by defining objective functions clearly and proposing some new objective-based rough clustering methods. In this paper, we introduce these methods classified into three categories, that is metric model, non-metric model and regression model. Moreover we discuss the features of these methods.