SpecVAT: Enhanced Visual Cluster Analysis

Given a pairwise dissimilarity matrix D of a set of objects, visual methods such as the VAT algorithm (for visual analysis of cluster tendency) represent (D macr )as an image (D macr ) where the objects are reordered to highlight cluster structure as dark blocks along the diagonal of the image. A major limitation of such visual methods is their inability to highlight cluster structure in 1(D macr ) when D contains clusters with highly complex structure. In this paper, we address this limitation by proposing a Spectral VAT (SpecVAT) algorithm, where D is mapped to D´ in an embedding space by spectral decomposition of the Laplacian matrix, and then reordered to D´ using the VAT algorithm. We also propose a strategy to automatically determine the number of clusters in (D macr ´), as well as a method for cluster formation from (D macr ´) based on the difference between diagonal blocks and off-diagonal blocks. We demonstrate the effectiveness of our algorithms on several synthetic and real-world data sets that are not amenable to analysis via traditional VAT.