In this extended abstract, we describe and analyze a lossy compression of MinHash from buckets of size $O(log n)$ to buckets of size $O(loglog n)$ 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 MinHashs 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 $Oleft(epsilon^{-2} left( loglog n + log frac{1}{ t epsilon} right)right)$ 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.
تحميل البحث