Improved Asymmetric Locality Sensitive Hashing (ALSH) for Maximum Inner Product Search (MIPS)

Abstract: Recently it was shown that the problem of Maximum Inner Product Search (MIPS) is efficient and it admits provably sub-linear hashing algorithms. Asymmetric transformations before hashing were the key in solving MIPS which was otherwise hard. In the prior work, the authors use asymmetric transformations which convert the problem of approximate MIPS into the problem of approximate near neighbor search which can be efficiently solved using hashing. In this work, we provide a different transformation which converts the problem of approximate MIPS into the problem of approximate cosine similarity search which can be efficiently solved using signed random projections. Theoretical analysis show that the new scheme is significantly better than the original scheme for MIPS. Experimental evaluations strongly support the theoretical findings.