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

TL;DR

This paper introduces the first provably sublinear time hashing algorithm for approximate Maximum Inner Product Search (MIPS), extending LSH to asymmetric schemes and demonstrating effectiveness in recommendation systems.

Contribution

It develops the first asymmetric hashing scheme for MIPS, overcoming limitations of traditional LSH, and provides a practical, provably fast algorithm for inner product search.

Findings

Achieves sublinear time approximate MIPS

Effective in collaborative filtering for recommendations

Extends LSH framework to asymmetric transformations

Abstract

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