On the region proximity in metric spaces

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The problem of defining a measure of proximity for regions of generic metric spaces, as needed for designing and implementing indexes for similarity retrieval, is investigated. Though the proposed probabilistic approach is valid for arbitrary regions, specific ready-to-use formulas are developed for the important case of ball regions, considering both the uniform and the actual distribution of objects' pair-wise distances. The theoretical results are verified by experiments. Possible applications of the approach to practical data and index management problems are discussed.