Cluster Analysis Using Rough Clustering and k-Means Clustering

Abstract

Cluster analysis is a fundamental data reduction technique used in the physical and social sciences. It is of potential interest to managers in Information Science, as it can be used to identify user needs though segmenting users such as Web site visitors. In addition, the theory of Rough sets is the subject of intense interest in computational intelligence research. The extension of this theory into rough clustering provides an important and potentially useful addition to the range of cluster analysis techniques available to the manager. Cluster analysis is defined as the grouping of “individuals or objects into clusters so that objects in the same cluster are more similar to one another than they are to objects in other clusters” (Hair, Black, Babin, Anderson, & Tatham, 2006). There are a number of comprehensive introductions to cluster analysis (Abonyi & Feil, 2007; Arabie, Hubert, & De Soete, 1994; Cramer, 2003; Everitt, Landau, & Leese, 2001; Gan, Ma, & Wu, 2007; Härdle & Hlávka, 2007). Techniques are often classified as hierarchical or nonhierarchical (Hair et al., 2006), and the most commonly used nonhierarchical technique is the k-means approach developed by MacQueen (1967). Recently, techniques based on developments in computational intelligence have also been used as clustering algorithms. For example, the theory of fuzzy sets developed by Zadeh (1965), which introduced the concept of partial set membership, has been applied to clustering (Abonyi & Feil, 2007; Dumitrescu, Lazzerini, & Jain, 2000). Another technique receiving considerable attention is the theory of rough sets (Pawlak, 1982), which has led to clustering algorithms referred to as rough clustering (do Prado, Engel, & Filho, 2002; Kumar, Krishna, Bapi, & De, 2007; Parmar, Wu, & Blackhurst, 2007; Voges, Pope, & Brown, 2002). This article provides brief introductions to k-means cluster analysis, rough sets theory, and rough clustering, and compares k-means clustering and rough clustering. It shows that rough clustering provides a more flexible solution to the clustering problem, and can be conceptualized as extracting concepts from the data, rather than strictly delineated subgroupings (Pawlak, 1991). Traditional clustering methods generate extensional descriptions of groups (i.e., which objects are members of each cluster), whereas clustering techniques based on rough sets theory generate intentional descriptions (i.e., what are the main characteristics of each cluster) (do Prado et al., 2002). These different goals suggest that both k-means clustering and rough clustering have their place in the data analyst’s and the information manager’s toolbox.