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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.

Clustering is one of the most relevant data mining tasks. Its goal is to group similar objects in one cluster while dissimilar objects should belong to different clusters. Many extensions have been developed based on traditional cluster algorithms. Recently, approaches for dynamic as well as for granular clustering have been of particular interest. This paper provides a framework, DCCDynamic Clustering Cube, to categorize existing dynamic granular clustering algorithms. Furthermore, the DCCFramework can be used as a research map and starting point for new developments in this area.

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Traditional clustering partitions a group of objects into a number of nonoverlapping sets based on a similarity measure. In real world, the boundaries of these sets or clusters may not be clearly defined. Some of the objects may be almost equidistant from the center of multiple clusters. Traditional set theory mandates that these objects be assigned to a single cluster. Rough set theory can be used to represent the overlapping clusters. Rough sets provide more flexible representation than conventional sets, at the same time they are less descriptive than the fuzzy sets. This paper describes the basic concept of rough clustering based on k‐means, genetic algorithms, Kohonen self‐organizing maps, and support vector clustering. The discussion also includes a review of rough cluster validity measures, and applications of rough clustering to such diverse areas as forestry, medicine, medical imaging, web mining, super markets, and traffic engineering. © 2011 John Wiley & Sons, Inc. WIREs Data Mining Knowl Discov 2011 1 64‐72 DOI: 10.1002/widm.16 This article is categorized under: Technologies > Computational Intelligence Technologies > Machine Learning Technologies > Structure Discovery and Clustering