Proceedings of the 15th ACM symposium on Access control models and technologies
iVAT and aVAT: enhanced visual analysis for cluster tendency assessment
PAKDD'10 Proceedings of the 14th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining - Volume Part I
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Given a pairwise dissimilarity matrix $\bm{D}$ of a set ofobjects, visual methods such as the VAT algorithm (for visual analysis of cluster tendency) represent $\bm{D}$ as an image $\mathrm{I}(\tilde{\bm{D}})$ 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 $\mathrm{I}(\tilde{\bm{D}})$ when $\bm{D}$ contains clusters with highly complex structure. In this paper, we address this limitation by proposing a Spectral VAT (SpecVAT) algorithm, where $\bm{D}$ is mapped to $\bm{D'}$ in an embedding space by spectral decomposition of the Laplacian matrix, and then reordered to $\bm{\tilde{D'}}$ using the VAT algorithm. We also propose astrategy to automatically determine the number of clusters in $\mathrm{I}(\bm{\tilde{D'}})$, as well as a method for cluster formation from $\mathrm{I}(\bm{\tilde{D'}})$ 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.