Toward Improving b-Coloring based Clustering using a Greedy re-Coloring Algorithm

Clustering is an important task in the process of data analysis which can be viewed as a data modeling technique that provides an attractive mechanism to automatically find the hidden structure of large data sets (Jain et al., 1999). Informally, this task consists of the division of data items (objects, instances, etc.) into groups or categories, such that all objects in the same group are similar to each other, while dissimilar from objects in the other groups. Clustering plays an important role in data mining applications such as Web analysis, information retrieval, medical diagnosis, and many other domains. Recently, we have proposed a clustering method based on the concept of b-coloring of a graph (Irving & Manlov, 1999). A graph b-coloring is an assignment of colors to the vertices of the graph such that: i. no two adjacent vertices (vertices joined by an weighted edge representing the dissimilarity between objects) have the same color (proper coloring) ii. for each color, there exists at least one vertex which is adjacent (has a sufficient dissimilarity degree) to all other colors. This vertex is called a dominating vertex; there can be many within the same class. Both (i) and (ii) are the constraints in b-coloring of a graph. The b-coloring based clustering method enables to build a fine partition of the dataset into clusters even when the number of clusters is not specified in advance. The previous clustering algorithm in (Elghazel et al., 2006) conducts the following two steps in greedy fashion: 1. initalizes the colors of vertices so that the colors satisfy proper coloring, and 2. removes, by a greedy procedure, the colors that have no dominating vertices, until each color has at least one dominating vertex. These steps correspond to the above two constraints in b-coloring. Although it returns a bcoloring of a graph, it does not explicitly consider the quality of the clusters in the algorithm. Thus, besides satisfying the above constraints, it was difficult to explicitly generate better clusters of the given data items. O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg