Optimal Smoothing of Kernel-Based Topographic Maps with Application to Density-Based Clustering of Shapes

A crucial issue when applying topographic maps for clustering purposes is how to select the map's overall degree of smoothness. In this paper, we develop a new strategy for optimally smoothing, by a common scale factor, the density estimates generated by Gaussian kernel-based topographic maps. We also introduce a new representation structure for images of shapes, and a new metric for clustering them. These elements are incorporated into a hierarchical, density-based clustering procedure. As an application, we consider the clustering of shapes of marine animals taken from the SQUID image database. The results are compared to those obtained with the CSS retrieval system developed by Mokhtarian and co-workers, and with the more familiar Euclidean distance-based clustering metric.

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