134 research outputs found
Improved Asymmetric Locality Sensitive Hashing (ALSH) for Maximum Inner Product Search (MIPS)
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.Comment: arXiv admin note: text overlap with arXiv:1405.586
When Hashing Met Matching: Efficient Spatio-Temporal Search for Ridesharing
Carpooling, or sharing a ride with other passengers, holds immense potential
for urban transportation. Ridesharing platforms enable such sharing of rides
using real-time data. Finding ride matches in real-time at urban scale is a
difficult combinatorial optimization task and mostly heuristic approaches are
applied. In this work, we mathematically model the problem as that of finding
near-neighbors and devise a novel efficient spatio-temporal search algorithm
based on the theory of locality sensitive hashing for Maximum Inner Product
Search (MIPS). The proposed algorithm can find near-optimal potential
matches for every ride from a pool of rides in time and space for a small . Our
algorithm can be extended in several useful and interesting ways increasing its
practical appeal. Experiments with large NY yellow taxi trip datasets show that
our algorithm consistently outperforms state-of-the-art heuristic methods
thereby proving its practical applicability
On Symmetric and Asymmetric LSHs for Inner Product Search
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 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.Comment: 11 pages, 3 figures, In Proceedings of The 32nd International
Conference on Machine Learning (ICML
SAH: Shifting-aware Asymmetric Hashing for Reverse -Maximum Inner Product Search
This paper investigates a new yet challenging problem called Reverse
-Maximum Inner Product Search (RMIPS). Given a query (item) vector, a set
of item vectors, and a set of user vectors, the problem of RMIPS aims to
find a set of user vectors whose inner products with the query vector are one
of the largest among the query and item vectors. We propose the first
subquadratic-time algorithm, i.e., Shifting-aware Asymmetric Hashing (SAH), to
tackle the RMIPS problem. To speed up the Maximum Inner Product Search
(MIPS) on item vectors, we design a shifting-invariant asymmetric
transformation and develop a novel sublinear-time Shifting-Aware Asymmetric
Locality Sensitive Hashing (SA-ALSH) scheme. Furthermore, we devise a new
blocking strategy based on the Cone-Tree to effectively prune user vectors (in
a batch). We prove that SAH achieves a theoretical guarantee for solving the
RMIPS problem. Experimental results on five real-world datasets show that SAH
runs 48 faster than the state-of-the-art methods for RMIPS
while achieving F1-scores of over 90\%. The code is available at
\url{https://github.com/HuangQiang/SAH}.Comment: Accepted by AAAI 202
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