843 research outputs found
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]
Finding Associations and Computing Similarity via Biased Pair Sampling
This version is ***superseded*** by a full version that can be found at
http://www.itu.dk/people/pagh/papers/mining-jour.pdf, which contains stronger
theoretical results and fixes a mistake in the reporting of experiments.
Abstract: Sampling-based methods have previously been proposed for the
problem of finding interesting associations in data, even for low-support
items. While these methods do not guarantee precise results, they can be vastly
more efficient than approaches that rely on exact counting. However, for many
similarity measures no such methods have been known. In this paper we show how
a wide variety of measures can be supported by a simple biased sampling method.
The method also extends to find high-confidence association rules. We
demonstrate theoretically that our method is superior to exact methods when the
threshold for "interesting similarity/confidence" is above the average pairwise
similarity/confidence, and the average support is not too low. Our method is
particularly good when transactions contain many items. We confirm in
experiments on standard association mining benchmarks that this gives a
significant speedup on real data sets (sometimes much larger than the
theoretical guarantees). Reductions in computation time of over an order of
magnitude, and significant savings in space, are observed.Comment: This is an extended version of a paper that appeared at the IEEE
International Conference on Data Mining, 2009. The conference version is (c)
2009 IEE
A Comparison of Blocking Methods for Record Linkage
Record linkage seeks to merge databases and to remove duplicates when unique
identifiers are not available. Most approaches use blocking techniques to
reduce the computational complexity associated with record linkage. We review
traditional blocking techniques, which typically partition the records
according to a set of field attributes, and consider two variants of a method
known as locality sensitive hashing, sometimes referred to as "private
blocking." We compare these approaches in terms of their recall, reduction
ratio, and computational complexity. We evaluate these methods using different
synthetic datafiles and conclude with a discussion of privacy-related issues.Comment: 22 pages, 2 tables, 7 figure
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