Selective Hashing: Closing the Gap between Radius Search and k-NN Search

Locality Sensitive Hashing (LSH) and its variants, are generally believed to be the most effective radius search methods in high-dimensional spaces. However, many applications involve finding the k nearest neighbors (k-NN), where the k-NN distances of different query points may differ greatly and the performance of LSH suffers. We propose a novel indexing scheme called Selective Hashing, where a disjoint set of indices are built with different granularities and each point is only stored in the most effective index. Theoretically, we show that k-NN search using selective hashing can achieve the same recall as a fixed radius LSH search, using a radius equal to the distance of the c1kth nearest neighbor, with at most c2 times overhead, where c1 and c2 are small constants. Selective hashing is also easy to build and update, and outperforms all the state-of-the-art algorithms such as DSH and IsoHash.

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