HyperMinHash: MinHash in LogLog space.

In this extended abstract, we describe and analyze a lossy compression of MinHash from buckets of size O ( l o g n ) to buckets of size O ( l o g l o g 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 an additive approximation error ϵ on a Jaccard index t , given a random oracle, HyperMinHash needs O ( ϵ - 2 ( l o g l o g n + l o g 1 ϵ ) ) 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 2MiB of memory; MinHash can only estimate Jaccard indices for cardinalities of 10 10 with the same memory consumption.