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Issue No.10 - October (2010 vol.22)
pp: 1401-1414
Liang Wang , The University of Melbourne, Melbourne
Xin Geng , Southeast University, Nanjing
James Bezdek , The University of Melbourne, Melbourne
Christopher Leckie , The University of Melbourne, Melbourne
Kotagiri Ramamohanarao , The University of Melbourne, Melbourne
Visual methods have been widely studied and used in data cluster analysis. Given a pairwise dissimilarity matrix {\schmi D} of a set of n objects, visual methods such as the VAT algorithm generally represent {\schmi D} as an n\times n image {\rm I}(\tilde{{\schmi D}}) 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 {\schmi D} contains highly complex clusters. This paper addresses this limitation by proposing a Spectral VAT algorithm, where {\schmi D} is mapped to {\schmi D}^{\prime } in a graph embedding space and then reordered to {{\tilde{\schmi D}^{\prime }}} using the VAT algorithm. A strategy for automatic determination of the number of clusters in {\rm I}({\tilde{{\schmi D}^{\prime }}}) is then proposed, as well as a visual method for cluster formation from {\rm I}({\tilde{{\schmi D}^{\prime }}}) 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, VAT, cluster tendency, spectral embedding, out-of-sample extension.
Liang Wang, Xin Geng, James Bezdek, Christopher Leckie, Kotagiri Ramamohanarao, "Enhanced Visual Analysis for Cluster Tendency Assessment and Data Partitioning", IEEE Transactions on Knowledge & Data Engineering, vol.22, no. 10, pp. 1401-1414, October 2010, doi:10.1109/TKDE.2009.192
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