Hausdorff Clustering

By Nicolas Basalto et al
Published on Jan. 7, 2008
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Table of Contents

I. INTRODUCTION
II. PRELIMINARES
A. Distances and pseudodistances
B. Linkage algorithms
III. COMPLETE AND SINGLE LINKAGE
A. "Distances"
B. Finite sets
C. Comments
IV. HAUSDORFF DISTANCE AND HAUSDORFF LINKAGE
A. Hausdorff distance
B. Hausdorff linkage

Summary

The document introduces a clustering algorithm based on the Hausdorff distance and compares it with single and complete linkage methods. It discusses the concepts of distance and pseudodistances in clustering algorithms. The complete linkage method tends to form compact clusters, while the single linkage method may lead to elongated clusters. The Hausdorff distance between sets A and B is defined as the largest distance a point in A is from B, and vice versa. The document also presents the Hausdorff linkage algorithm based on this distance measure. The Hausdorff distance is shown to be a metric on the set K(S) of nonempty compact subsets of a metric space. It ensures completeness in the space (K(S), dH). The document highlights the advantages of using the Hausdorff distance for clustering complex and large sets, providing a more accurate clustering approach.
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