Polytopes, lattices, and spherical codes for the nearest neighbor problem

10 Jul 2019Thijs Laarhoven

We study locality-sensitive hash methods for the nearest neighbor problem for the angular distance, focusing on the approach of first projecting down onto a low-dimensional subspace, and then partitioning the projected vectors according to Voronoi cells induced by a suitable spherical code. This approach generalizes and interpolates between the fast but suboptimal hyperplane hashing of Charikar [STOC'02] and the asymptotically optimal but practically often slower hash families of Andoni-Indyk [FOCS'06], Andoni-Indyk-Nguyen-Razenshteyn [SODA'14] and Andoni-Indyk-Laarhoven-Razenshteyn-Schmidt [NIPS'15]... (read more)

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