Measures for clustering and anomaly detection in sets of higher dimensional ellipsoids

One of the applications that motivates this research is a system for detection of the anomalies in wireless sensor networks (WSNs). Individual sensor measurements are converted to ellipsoidal summaries; a data matrix D is built using a dissimilarity measure between pairs of ellipsoids; clusters of ellipsoids are suggested by dark blocks along the diagonal of an iVAT (improved Visual Assessment of Tendency) image of D; and finally, the single linkage algorithm extracts clusters from D, using the iVAT image as a guide to the selection of an optimal partition. We illustrate this model for higher dimensional data with synthetic, real and benchmark data sets. Our examples show that two of the four measures, viz, Focal distance and Bhattacharyya distance, provide very similar and reliable bases for estimating cluster structures in sets of higher dimensional ellipsoids, that single linkage can successfully extract the indicated clusters, and that our model can find both first and second order anomalies in WSN data.