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

Recently we showed that the problem of Maximum Inner Product Search (MIPS) is efficient and it admits provably sub-linear hashing algorithms. In [23], we used asymmetric transformations to convert the problem of approximate MIPS into the problem of approximate near neighbor search which can be efficiently solved using L2-LSH. In this paper, we revisit the problem of MIPS and argue that the quantizations used in L2-LSH is suboptimal for MIPS compared to signed random projections (SRP) which is another popular hashing scheme for cosine similarity (or correlations). Based on this observation, we provide different asymmetric transformations which convert the problem of approximate MIPS into the problem amenable to SRP instead of L2-LSH. An additional advantage of our scheme is that we also obtain LSH type space partitioning which is not possible with the existing scheme. Our theoretical analysis shows that the new scheme is significantly better than the original scheme for MIPS. Experimental evaluations strongly support the theoretical findings. In addition, we also provide the first empirical comparison that shows the superiority of hashing over tree based methods [21] for MIPS.