Clustering ellipses for anomaly detection

  • Moshtaghi M
  • Havens T
  • Bezdek J
 et al. 
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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. © 2010 Elsevier Ltd. All rights reserved.

Author-supplied keywords

  • Cluster analysis
  • Elliptical anomalies in wireless sensor networks
  • Reordered dissimilarity images
  • Similarity of ellipsoids
  • Single linkage clustering
  • Visual assessment

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Authors

  • Masud Moshtaghi

  • Timothy C. Havens

  • James C. Bezdek

  • Laurence Park

  • Christopher Leckie

  • Sutharshan Rajasegarar

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