An Efficient Formulation of the Improved Visual Assessment of Cluster Tendency (iVAT) Algorithm

The VAT algorithm is a visual method for determining the possible number of clusters in, or the cluster tendency of a set of objects. The improved VAT (iVAT) algorithm uses a graph-theoretic distance transform to improve the effectiveness of the VAT algorithm for “tough” cases where VAT fails to accurately show the cluster tendency. In this paper, we present an efficient formulation of the iVAT algorithm which reduces the computational complexity of the iVAT algorithm from O(N³) to O(N²). We also prove a direct relationship between the VAT image and the iVAT image produced by our efficient formulation. We conclude with three examples displaying clustering tendencies in three of the Karypis data sets that illustrate the improvement offered by the iVAT transformation. We also provide a comparison of iVAT images to those produced by the Reverse Cuthill-Mckee (RCM) algorithm; our examples suggest that iVAT is superior to the RCM method of display.