AdaLSH: Adaptive LSH for Solving c-Approximate Maximum Inner Product Search Problem

Maximum inner product search (MIPS) problem has gained much attention in a wide range of applications. In order to overcome the curse of dimensionality in high-dimensional spaces, most of existing methods first transform the MIPS problem into another approximate nearest neighbor search (ANNS) problem and then solve it by Locality Sensitive Hashing (LSH). However, due to the error incurred by the transmission and incomprehensive search strategies, these methods suffer from low precision and have loose probability guarantees. In this paper, we propose a novel search method named Adaptive-LSH (AdaLSH) to solve MIPS problem more efficiently and more precisely. AdaLSH examines objects in the descending order of both norms and (the probably correctly estimated) cosine angles with a query object in support of LSH with extendable windows. Such extendable windows bring not only efficiency in searching but also the probability guarantee of finding exact or approximate MIP objects. AdaLSH gives a better probability guarantee of success than those in conventional algorithms, bringing less running times on various datasets compared with them. In addition, AdaLSH can even support exact MIPS with probability guarantee.