Asymmetric LSH (ALSH) for Sublinear Time Maximum Inner Product Search (MIPS)

摘要

We present the first provably sublinear time algorithm for approximate\emph{Maximum Inner Product Search} (MIPS). Our proposal is also the firsthashing algorithm for searching with (un-normalized) inner product as theunderlying similarity measure. Finding hashing schemes for MIPS was consideredhard. We formally show that the existing Locality Sensitive Hashing (LSH)framework is insufficient for solving MIPS, and then we extend the existing LSHframework to allow asymmetric hashing schemes. Our proposal is based on aninteresting mathematical phenomenon in which inner products, after independentasymmetric transformations, can be converted into the problem of approximatenear neighbor search. This key observation makes efficient sublinear hashingscheme for MIPS possible. In the extended asymmetric LSH (ALSH) framework, weprovide an explicit construction of provably fast hashing scheme for MIPS. Theproposed construction and the extended LSH framework could be of independenttheoretical interest. Our proposed algorithm is simple and easy to implement.We evaluate the method, for retrieving inner products, in the collaborativefiltering task of item recommendations on Netflix and Movielens datasets.