5,131 research outputs found
Hashing for Similarity Search: A Survey
Similarity search (nearest neighbor search) is a problem of pursuing the data
items whose distances to a query item are the smallest from a large database.
Various methods have been developed to address this problem, and recently a lot
of efforts have been devoted to approximate search. In this paper, we present a
survey on one of the main solutions, hashing, which has been widely studied
since the pioneering work locality sensitive hashing. We divide the hashing
algorithms two main categories: locality sensitive hashing, which designs hash
functions without exploring the data distribution and learning to hash, which
learns hash functions according the data distribution, and review them from
various aspects, including hash function design and distance measure and search
scheme in the hash coding space
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
Tradeoffs for nearest neighbors on the sphere
We consider tradeoffs between the query and update complexities for the
(approximate) nearest neighbor problem on the sphere, extending the recent
spherical filters to sparse regimes and generalizing the scheme and analysis to
account for different tradeoffs. In a nutshell, for the sparse regime the
tradeoff between the query complexity and update complexity
for data sets of size is given by the following equation in
terms of the approximation factor and the exponents and :
For small , minimizing the time for updates leads to a linear
space complexity at the cost of a query time complexity .
Balancing the query and update costs leads to optimal complexities
, matching bounds from [Andoni-Razenshteyn, 2015] and [Dubiner,
IEEE-TIT'10] and matching the asymptotic complexities of [Andoni-Razenshteyn,
STOC'15] and [Andoni-Indyk-Laarhoven-Razenshteyn-Schmidt, NIPS'15]. A
subpolynomial query time complexity can be achieved at the cost of a
space complexity of the order , matching the bound
of [Andoni-Indyk-Patrascu, FOCS'06] and
[Panigrahy-Talwar-Wieder, FOCS'10] and improving upon results of
[Indyk-Motwani, STOC'98] and [Kushilevitz-Ostrovsky-Rabani, STOC'98].
For large , minimizing the update complexity results in a query complexity
of , improving upon the related exponent for large of
[Kapralov, PODS'15] by a factor , and matching the bound
of [Panigrahy-Talwar-Wieder, FOCS'08]. Balancing the costs leads to optimal
complexities , while a minimum query time complexity can be
achieved with update complexity , improving upon the
previous best exponents of Kapralov by a factor .Comment: 16 pages, 1 table, 2 figures. Mostly subsumed by arXiv:1608.03580
[cs.DS] (along with arXiv:1605.02701 [cs.DS]
Coding for Random Projections
The method of random projections has become very popular for large-scale
applications in statistical learning, information retrieval, bio-informatics
and other applications. Using a well-designed coding scheme for the projected
data, which determines the number of bits needed for each projected value and
how to allocate these bits, can significantly improve the effectiveness of the
algorithm, in storage cost as well as computational speed. In this paper, we
study a number of simple coding schemes, focusing on the task of similarity
estimation and on an application to training linear classifiers. We demonstrate
that uniform quantization outperforms the standard existing influential method
(Datar et. al. 2004). Indeed, we argue that in many cases coding with just a
small number of bits suffices. Furthermore, we also develop a non-uniform 2-bit
coding scheme that generally performs well in practice, as confirmed by our
experiments on training linear support vector machines (SVM)
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