Enhanced Visual Analysis for Cluster Tendency Assessment and Data Partitioning
Visual methods have been widely studied and used in data cluster analysis. Given a pairwise dissimilarity matrix D of a set of n objects, visual methods such as the VAT algorithm generally represent D as an n x n image I((D) over bar) where the objects are reordered to reveal hidden cluster structure as dark blocks along the diagonal of the image. A major limitation of such methods is their inability to highlight cluster structure when D contains highly complex clusters. This paper addresses this limitation by proposing a Spectral VAT algorithm, where D is mapped to D' in a graph embedding space and then reordered to (D) over tilde using the VAT algorithm. A strategy for automatic determination of the number of clusters in I (D) over tilde' is then proposed, as well as a visual method for cluster formation from I((D) over tilde)' based on the difference between diagonal blocks and off-diagonal blocks. A sampling-based extended scheme is also proposed to enable visual cluster analysis for large data sets. Extensive experimental results on several synthetic and real-world data sets validate our algorithms.
clustering cluster tendency vat spectral embedding out-of-sample extension