MIPS is a challenging problem as modern datasets often have high dimensionality and large cardinality. Initially, tree-based methods [Ram and Gray, 2012, Koenigstein et al., 2012] were proposed for MIPS, which use the idea of branch and bound similar to k-d tree [Friedman and Tukey, 1974].

MIPS is a challenging problem as modern datasets often have high dimensionality and large cardinality. Initially, tree-based methods [Ram and Gray, 2012, Koenigstein et al., 2012] were proposed for MIPS, which use the idea of branch and bound similar to k-d tree [Friedman and Tukey, 1974].

We present the first provably sublinear time hashing algorithm for approximate \emph{Maximum Inner Product Search} (MIPS). Searching with (un-normalized) inner product as the underlying similarity measure is a known difficult problem and finding hashing schemes for MIPS was considered hard. While the existing Locality Sensitive Hashing (LSH) framework is insufficient for solving MIPS, in this paper we extend the LSH framework to allow asymmetric hashing schemes. Our proposal is based on a key observation that the problem of finding maximum inner products, after independent asymmetric transformations, can be converted into the problem of approximate near neighbor search in classical settings. This key observation makes efficient sublinear hashing scheme for MIPS possible. Under the extended asymmetric LSH (ALSH) framework, this paper provides an example of explicit construction of provably fast hashing scheme for MIPS. Our proposed algorithm is simple and easy to implement. The proposed hashing scheme leads to significant computational savings over the two popular conventional LSH schemes: (i) Sign Random Projection (SRP) and (ii) hashing based on $p$-stable distributions for $L_2$ norm (L2LSH), in the collaborative filtering task of item recommendations on Netflix and Movielens (10M) datasets.

We present the first provably sublinear time hashing algorithm for approximate Maximum Inner Product Search (MIPS). Searching with (un-normalized) inner product as the underlying similarity measure is a known difficult problem and finding hashing schemes for MIPS was considered hard. While the existing Locality Sensitive Hashing (LSH) framework is insufficient for solving MIPS, in this paper we extend the LSH framework to allow asymmetric hashing schemes. Our proposal is based on a key observation that the problem of finding maximum inner products, after independent asymmetric transformations, can be converted into the problem of approximate near neighbor search in classical settings. This key observation makes efficient sublinear hashing scheme for MIPS possible. Under the extended asymmetric LSH (ALSH) framework, this paper provides an example of explicit construction of provably fast hashing scheme for MIPS. Our proposed algorithm is simple and easy to implement.

We present the first provably sublinear time hashing algorithm for approximate Maximum Inner Product Search (MIPS). Searching with (un-normalized) inner product as the underlying similarity measure is a known difficult problem and finding hashing schemes for MIPS was considered hard. While the existing Locality Sensitive Hashing (LSH) framework is insufficient for solving MIPS, in this paper we extend the LSH framework to allow asymmetric hashing schemes. Our proposal is based on a key observation that the problem of finding maximum inner products, after independent asymmetric transformations, can be converted into the problem of approximate near neighbor search in classical settings. This key observation makes efficient sublinear hashing scheme for MIPS possible. Under the extended asymmetric LSH (ALSH) framework, this paper provides an example of explicit construction of provably fast hashing scheme for MIPS. Our proposed algorithm is simple and easy to implement.

We present the first provably sublinear time hashing algorithm for approximate \emph{Maximum Inner Product Search} (MIPS). Searching with (un-normalized) inner product as the underlying similarity measure is a known difficult problem and finding hashing schemes for MIPS was considered hard. While the existing Locality Sensitive Hashing (LSH) framework is insufficient for solving MIPS, in this paper we extend the LSH framework to allow asymmetric hashing schemes. Our proposal is based on a key observation that the problem of finding maximum inner products, after independent asymmetric transformations, can be converted into the problem of approximate near neighbor search in classical settings. This key observation makes efficient sublinear hashing scheme for MIPS possible.

Neyshabur and Srebro proposed Simple-LSH, which is the state-of-the-art hashing method for maximum inner product search (MIPS) with performance guarantee. We found that the performance of Simple-LSH, in both theory and practice, suffers from long tails in the 2-norm distribution of real datasets. We propose Norm-ranging LSH, which addresses the excessive normalization problem caused by long tails in Simple-LSH by partitioning a dataset into multiple sub-datasets and building a hash index for each sub-dataset independently. We prove that Norm-ranging LSH has lower query time complexity than Simple-LSH. We also show that the idea of partitioning the dataset can improve other hashing based methods for MIPS. To support efficient query processing on the hash indexes of the sub-datasets, a novel similarity metric is formulated. Experiments show that Norm-ranging LSH achieves an order of magnitude speedup over Simple-LSH for the same recall, thus significantly benefiting applications that involve MIPS.

We consider the problem of designing locality sensitive hashes (LSH) for inner product similarity, and of the power of asymmetric hashes in this context. Shrivastava and Li (2014a) argue that there is no symmetric LSH for the problem and propose an asymmetric LSH based on different mappings for query and database points. However, we show there does exist a simple symmetric LSH that enjoys stronger guarantees and better empirical performance than the asymmetric LSH they suggest. We also show a variant of the settings where asymmetry is in-fact needed, but there a different asymmetric LSH is required.

We present the first provably sublinear time hashing algorithm for approximate \emph{Maximum Inner Product Search} (MIPS). Searching with (un-normalized) inner product as the underlying similarity measure is a known difficult problem and finding hashing schemes for MIPS was considered hard. While the existing Locality Sensitive Hashing (LSH) framework is insufficient for solving MIPS, in this paper we extend the LSH framework to allow asymmetric hashing schemes. Our proposal is based on a key observation that the problem of finding maximum inner products, after independent asymmetric transformations, can be converted into the problem of approximate near neighbor search in classical settings. This key observation makes efficient sublinear hashing scheme for MIPS possible. Under the extended asymmetric LSH (ALSH) framework, this paper provides an example of explicit construction of provably fast hashing scheme for MIPS. Our proposed algorithm is simple and easy to implement. The proposed hashing scheme leads to significant computational savings over the two popular conventional LSH schemes: (i) Sign Random Projection (SRP) and (ii) hashing based on $p$-stable distributions for $L_2$ norm (L2LSH), in the collaborative filtering task of item recommendations on Netflix and Movielens (10M) datasets.