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Nearest neighbor searching of large databases in high-dimensional spaces isinherently difficult due to the curse of dimensionality. A flavor ofapproximation is, therefore, necessary to practically solve the problem ofnearest neighbor search. In this paper, we propose a novel yet simple indexingscheme, HD-Index, to solve the problem of approximate k-nearest neighborqueries in massive high-dimensional databases. HD-Index consists of a set ofnovel hierarchical structures called RDB-trees built on Hilbert keys ofdatabase objects. The leaves of the RDB-trees store distances of databaseobjects to reference objects, thereby allowing efficient pruning using distancefilters. In addition to triangular inequality, we also use Ptolemaic inequalityto produce better lower bounds. Experiments on massive (up to billion scale)high-dimensional (up to 1000+) datasets show that HD-Index is effective,efficient, and scalable.

HD-Index: Pushing the Scalability-Accuracy Boundary for Approximate kNN Search in High-Dimensional Spaces