We propose a new approach to perform approximate similarity search in metric spaces. The idea at the basis of this technique is that when two objects are very close one to each other they 'see' the world around them in the same way. Accordingly, we can use a measure of dissimilarity between the view of the world, from the perspective of the two objects, in place of the distance function of the underlying metric space. To exploit this idea we represent each object of a dataset by the ordering of a number of reference objects of the metric space according to their distance from the object itself. In order to compare two objects of the dataset we compare the two corresponding orderings of the reference objects. We show that efficient and effective approximate similarity searching can be obtained by using inverted files, relying on this idea. We show that the proposed approach performs better than other approaches in literature.
Similarity search structures for metric data typically bound object partitions by ball regions. Since regions can overlap, a relevant issue is to estimate the proximity of regions in order to predict the number of objects in the regions' intersection. This paper analyzes the problem using a probabilistic approach and provides a solution that effectively computes the proximity through realistic heuristics that only require small amounts of auxiliary data. An extensive simulation to validate the technique is provided. An application is developed to demonstrate how the proximity measure can be successfully applied to the approximate similarity search. Search speedup is achieved by ignoring data regions whose proximity to the query region is smaller than a user-defined threshold. This idea is implemented in a metric tree environment for the similarity range and "nearest neighbors" queries. Several measures of efficiency and effectiveness are applied to evaluate proposed approximate search algorithms on real-life data sets. An analytical model is developed to relate proximity parameters and the quality of search. Improvements of two orders of magnitude are achieved for moderately approximated search results. We demonstrate that the precision of proximity measures can significantly influence the quality of approximated algorithms.
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