HyperMinHash: MinHash in LogLog Space

Abstract

In this extended abstract, we describe and analyze a lossy compression of MinHash from buckets of size O(logn) to buckets of size O(log) 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 additive approximation error on a Jaccard index t, given a random oracle, HyperMinHash needs O-2(\log n + 1)Oϵ-2loglogn+log1ϵ space. HyperMinHash allows estimating Jaccard indices of 0.01 for set cardinalities on the order of 1019 with relative error of around 10 percent using 2MiB of memory; MinHash can only estimate Jaccard indices for cardinalities of 1010 with the same memory consumption.