Related papers: Lower bounds on Locality Sensitive Hashing
A Locality-Sensitive Hash (LSH) function is called $(r,cr,p_1,p_2)$-sensitive, if two data-points with a distance less than $r$ collide with probability at least $p_1$ while data points with a distance greater than $cr$ collide with…
We study lower bounds for Locality Sensitive Hashing (LSH) in the strongest setting: point sets in {0,1}^d under the Hamming distance. Recall that here H is said to be an (r, cr, p, q)-sensitive hash family if all pairs x, y in {0,1}^d with…
The Indyk-Motwani Locality-Sensitive Hashing (LSH) framework (STOC 1998) is a general technique for constructing a data structure to answer approximate near neighbor queries by using a distribution $\mathcal{H}$ over locality-sensitive hash…
Locality sensitive hashing (LSH) was introduced by Indyk and Motwani (STOC `98) to give the first sublinear time algorithm for the c-approximate nearest neighbor (ANN) problem using only polynomial space. At a high level, an LSH family…
For a metric space $(X, d)$, a family $\mathcal{H}$ of locality sensitive hash functions is called $(r, cr, p_1, p_2)$ sensitive if a randomly chosen function $h\in \mathcal{H}$ has probability at least $p_1$ (at most $p_2$) to map any $a,…
We present a new locality sensitive hashing (LSH) algorithm for $c$-approximate nearest neighbor search in $\ell_p$ with $1<p<2$. For a database of $n$ points in $\ell_p$, we achieve $O(dn^{\rho})$ query time and $O(dn+n^{1+\rho})$ space,…
We prove a tight lower bound for the exponent $\rho$ for data-dependent Locality-Sensitive Hashing schemes, recently used to design efficient solutions for the $c$-approximate nearest neighbor search. In particular, our lower bound matches…
We present a new data structure for the c-approximate near neighbor problem (ANN) in the Euclidean space. For n points in R^d, our algorithm achieves O(n^{\rho} + d log n) query time and O(n^{1 + \rho} + d log n) space, where \rho <=…
Locality-sensitive hashing (LSH), introduced by Indyk and Motwani in STOC '98, has been an extremely influential framework for nearest neighbor search in high-dimensional data sets. While theoretical work has focused on the approximate…
Similarity search in high-dimensional spaces is an important task for many multimedia applications. Due to the notorious curse of dimensionality, approximate nearest neighbor techniques are preferred over exact searching techniques since…
Locality Sensitive Hashing (LSH) is an effective method to index a set of points such that we can efficiently find the nearest neighbors of a query point. We extend this method to our novel Set-query LSH (SLSH), such that it can find the…
We show an optimal data-dependent hashing scheme for the approximate near neighbor problem. For an $n$-point data set in a $d$-dimensional space our data structure achieves query time $O(d n^{\rho+o(1)})$ and space $O(n^{1+\rho+o(1)} +…
Nearest neighbors search is a fundamental problem in various research fields like machine learning, data mining and pattern recognition. Recently, hashing-based approaches, e.g., Locality Sensitive Hashing (LSH), are proved to be effective…
In this paper we study the problem of finding the approximate nearest neighbor of a query point in the high dimensional space, focusing on the Euclidean space. The earlier approaches use locality-preserving hash functions (that tend to map…
In this paper, we show a construction of locality-sensitive hash functions without false negatives, i.e., which ensure collision for every pair of points within a given radius $R$ in $d$ dimensional space equipped with $l_p$ norm when $p…
Finding nearest neighbors in high-dimensional spaces is a fundamental operation in many diverse application domains. Locality Sensitive Hashing (LSH) is one of the most popular techniques for finding approximate nearest neighbor searches in…
Locality-sensitive hashing~[Indyk,Motwani'98] is a classical data structure for approximate nearest neighbor search. It allows, after a close to linear time preprocessing of the input dataset, to find an approximately nearest neighbor of…
The probability Jaccard similarity was recently proposed as a natural generalization of the Jaccard similarity to measure the proximity of sets whose elements are associated with relative frequencies or probabilities. In combination with a…
LSH (locality sensitive hashing) had emerged as a powerful technique in nearest-neighbor search in high dimensions [IM98, HIM12]. Given a point set $P$ in a metric space, and given parameters $r$ and $\varepsilon > 0$, the task is to…
We consider a new construction of locality-sensitive hash functions for Hamming space that is \emph{covering} in the sense that is it guaranteed to produce a collision for every pair of vectors within a given radius $r$. The construction is…