Evolutionary Rough k-Medoid Clustering

Abstract

Abstract. Recently, clustering algorithms based on rough set theory have gained increasing attention. For example, Lingras et al. introduced a rough k-means that assigns objects to lower and upper approximations of clusters. The objects in the lower approximation surely belong to a cluster while the membership of the objects in an upper approximation is uncertain. Therefore, the core cluster, defined by the objects in the lower approximation is surrounded by a buffer or boundary set with objects with unclear membership status. In this paper, we introduce an evolutionary rough k-medoid clustering algorithm. Evolutionary rough k-medoid clustering belongs to the families of Lingras' rough k-means and classic k-medoids algorithms. We apply the evolutionary rough k-medoids to synthetic as well as to real data sets and compare the results to Lingras' rough k-means. We also introduce a rough version of the Davies-Bouldin-Index as a cluster validity index for the family of rough clustering algorithms.

Uncertainty modeling in dynamic clustering — A soft computing perspective

“…Several extensions and modifications have been suggested in the meantime, e.g. in [12], [21], [22], [23], [24]. Areas of applications include bioinformatics [22], forest data [23] and web data analysis [19] besides others.…”

A class of dynamic rough partitive algorithms

“…Mitra et al 14 also introduced a hybrid rough‐fuzzy collaborative clustering algorithm. Applications of the class of Lingras' rough k ‐means have been presented by, for example, Mitra 8 and Peters et al15…”

Evolutionary and Iterative Crisp and Rough Clustering I: Theory

“…Unlike K-means algorithm where mean value is used as a centroid of a cluster, in K-medoid algorithm actual object is used as a reference point of a cluster [15]. A medoid is the most centrally located object in a given cluster.…”

“…Use of GAs for clustering is proposed by [2][9] [11]. GA guided evolutionary algorithms are also proposed for rough set and fuzzy clustering [8][12] [15].…”