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• W2950458457 abstract "We consider the problem of approximate set similarity search under Braun-Blanquet similarity $B(mathbf{x}, mathbf{y}) = |mathbf{x} cap mathbf{y}| / max(|mathbf{x}|, |mathbf{y}|)$. The $(b_2, b_2)$-approximate Braun-Blanquet similarity search problem is to preprocess a collection of sets $P$ such that, given a query set $mathbf{q}$, if there exists $mathbf{x} in P$ with $B(mathbf{q}, mathbf{x}) geq b_1$, then we can efficiently return $mathbf{x}' in P$ with $B(mathbf{q}, mathbf{x}') > b_2$. We present a simple data structure that solves this problem with space usage $O(n^{1+rho}log n + sum_{mathbf{x} in P}|mathbf{x}|)$ and query time $O(|mathbf{q}|n^{rho} log n)$ where $n = |P|$ and $rho = log(1/b_1)/log(1/b_2)$. Making use of existing lower bounds for locality-sensitive hashing by O'Donnell et al. (TOCT 2014) we show that this value of $rho$ is tight across the parameter space, i.e., for every choice of constants $0 < b_2 < b_1 < 1$. In the case where all sets have the same size our solution strictly improves upon the value of $rho$ that can be obtained through the use of state-of-the-art data-independent techniques in the Indyk-Motwani locality-sensitive hashing framework (STOC 1998) such as Broder's MinHash (CCS 1997) for Jaccard similarity and Andoni et al.'s cross-polytope LSH (NIPS 2015) for cosine similarity. Surprisingly, even though our solution is data-independent, for a large part of the parameter space we outperform the currently best data-dependent method by Andoni and Razenshteyn (STOC 2015)." @default.
• W2950458457 created "2019-06-27" @default.
• W2950458457 creator A5014293815 @default.
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• W2950458457 date "2016-12-22" @default.
• W2950458457 modified "2023-09-27" @default.
• W2950458457 title "Set Similarity Search Beyond MinHash" @default.
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