Discovery of Clusters from Proximity Data: An Approach Using Iterative Adjustment of Binary Classifications

Clustering is a task of forming groups of similar objects based on the predefined proximity (similarity/dissimilarity) measure and grouping criteria. A lot of approaches, for example, agglomerative/divisive hierarchical clustering, k-means and EM algorithms, have been proposed in the literature [1,2] and widely used for exploratory analysis of real-world data. In order to find the best partition of objects that maximizes both inter-cluster homogeneity and between-clusters isolation, clustering methods often employ geometric measures such as the variance of distances. However, it becomes difficult to form appropriate clusters if only a proximity matrix is available as intrinsic information for analysis and the raw attribute values of data are unavailable or inaccessible. This is because the lack of attribute-value information may bring a difficulty in computing the global properties of groups such as centroids. Additionally, the choice of global coherence/isolation measures is limited if the proximity is defined as a subjective or relative measure, because such a measure may not satisfy the triangular inequality for any triplet of objects. Although conventional hierarchical clusterings are known to be able to deal with relative or subjective measures, they involve other problems such as erosion or expansion of data space by intermediate objects between large clusters and the results are dependent on the orders of object handling [1].