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arXiv · 1710.08436

HyperMinHash: MinHash in LogLog space

Yun William Yu·Griffin M. Weber
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Abstract

In this extended abstract, we describe and analyze a lossy compression of MinHash from buckets of size $O(\log n)$ to buckets of size $O(\log\log n)$ by encoding using floating-point notation. This new compressed sketch, which we call HyperMinHash, as we build off a HyperLogLog scaffold, can be used as a drop-in replacement of MinHash. Unlike comparable Jaccard index fingerprinting algorithms in sub-logarithmic space (such as b-bit MinHash), HyperMinHash retains MinHash's features of streaming updates, unions, and cardinality estimation. For a multiplicative approximation error $1+ \epsilon$ on a Jaccard index $ t $, given a random oracle, HyperMinHash needs $O\left(\epsilon^{-2} \left( \log\log n + \log \frac{1}{ t \epsilon} \right)\right)$ space. HyperMinHash allows estimating Jaccard indices of 0.01 for set cardinalities on the order of $10^{19}$ with relative error of around 10\% using 64KiB of memory; MinHash can only estimate Jaccard indices for cardinalities of $10^{10}$ with the same memory consumption.

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Yun William Yu, Griffin M. Weber. 2017-10-23. HyperMinHash: MinHash in LogLog space. https://arxiv.org/abs/1710.08436

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