Clustering ellipses for anomaly detection

Authors:
Masud Moshtaghi;Timothy C. Havens;James C. Bezdek;Laurence Park;Christopher Leckie;Sutharshan Rajasegarar;James M. Keller;Marimuthu Palaniswami
Affiliations:
Department of Computer Science and Software Engineering, University of Melbourne, Parkville, Melbourne, Australia and NICTA Victoria Research Laboratories, Australia;Department of Electrical and Computer Engineering, University of Missouri, Columbia, MO 65211, USA;Department of Computer Science and Software Engineering, University of Melbourne, Parkville, Melbourne, Australia and Department of Electrical and Computer Engineering, University of Missouri, Col ...;School of Computing and Mathematics, University of Western Sydney, Australia;Department of Computer Science and Software Engineering, University of Melbourne, Parkville, Melbourne, Australia and NICTA Victoria Research Laboratories, Australia;Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, Melbourne, Australia;Department of Electrical and Computer Engineering, University of Missouri, Columbia, MO 65211, USA;Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, Melbourne, Australia
Venue:
Pattern Recognition
Year:
2011

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Abstract

Comparing, clustering and merging ellipsoids are problems that arise in various applications, e.g., anomaly detection in wireless sensor networks and motif-based patterned fabrics. We develop a theory underlying three measures of similarity that can be used to find groups of similar ellipsoids in p-space. Clusters of ellipsoids are suggested by dark blocks along the diagonal of a reordered dissimilarity image (RDI). The RDI is built with the recursive iVAT algorithm using any of the three (dis) similarity measures as input and performs two functions: (i) it is used to visually assess and estimate the number of possible clusters in the data; and (ii) it offers a means for comparing the three similarity measures. Finally, we apply the single linkage and CLODD clustering algorithms to three two-dimensional data sets using each of the three dissimilarity matrices as input. Two data sets are synthetic, and the third is a set of real WSN data that has one known second order node anomaly. We conclude that focal distance is the best measure of elliptical similarity, iVAT images are a reliable basis for estimating cluster structures in sets of ellipsoids, and single linkage can successfully extract the indicated clusters.