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Similarity Search on a Large Collection of Point Sets (2011)
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BibTeX
@MISC{Adelfio11similaritysearch,
author = {Marco D. Adelfio and Sarana Nutanong and Hanan Samet},
title = { Similarity Search on a Large Collection of Point Sets},
year = {2011}
}
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Abstract
Spatial applications often require the ability to perform similarity search over a collection of point sets. For example, given a geographical distribution of a disease outbreak, find k historical outbreaks with similar spatial distributions from a data collection D. In this paper, we study the problem of similarity search over a collection of point sets using the Hausdorff distance, which is a measure commonly used to determine the maximum discrepancy between two point sets. To avoid computing the Hausdorff distance for all point sets S in D, one may compute an optimistic estimate (i.e., lower bound value) of the actual Hausdorff distance HausDist(Q,S) for each S to rule out sets that are obviously dissimilar to Q. In our investigation, we observed that a commonly used method (called BscLB) to compute an estimate may not produce a result which is indicative of the actual Hausdorff distance. Consequently, we propose a method (called EnhLB) which produces a tighter estimate than the existing one. We then formulate a similarity search algorithm which uses a combination of BscLB and EnhLB to find similar point sets efficiently. In addition, we also extend our method to support an outlier-resistant variant of the Hausdorff distance called the modified Hausdorff distance. We compare our proposed algorithm with an algorithm using only BscLB. The results of our experiments show a reduction in computation time of 72 % for searches using the Hausdorff distance and a reduction of 53 % using the modified Hausdorff distance.
Keyphrases
point set hausdorff distance similarity search large collection maximum discrepancy actual hausdorff distance spatial application geographical distribution disease outbreak similar point set actual hausdorff distance hausdist outlier-resistant variant data collection similarity search algorithm historical outbreak tighter estimate similar spatial distribution computation time optimistic estimate
