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The estimated Jaccard similarity of two signatures.

public static double Jaccard(ReadOnlySpan<uint> left, ReadOnlySpan<uint> right)

Parameters — left and right are two signatures of the same non-zero length, built from the same permutations.

Returns — double, the share of slots that agree, in [0, 1].

Exceptions — ArgumentException when the two are not the same non-zero length.

Example — disjoint sets estimate zero.

using Lodestar.Text.Similarity;

var hasher = new MinHash(new MinHashPermutations([3UL, 5UL, 7UL, 11UL], [13UL, 17UL, 19UL, 23UL]));

uint[] left = hasher.Signature(["alpha", "beta"]);
uint[] right = hasher.Signature(["gamma", "delta"]);

double estimate = MinHash.Jaccard(left, right);  // => 0

Remarks — an estimate, not the Jaccard index. It is unbiased, and its standard error is about 1 / sqrt(Length) — 128 permutations put it near 0.09, which is why a threshold and a signature length are chosen together rather than separately.

Signatures built from different permutations are not comparable, and nothing here can detect that: the lengths match, the values are hashes, and the answer comes back looking ordinary. One MinHashPermutations per index is the discipline that avoids it.

The exact Jaccard index over the sets themselves is Jaccard.Similarity, which is what to use when the sets are small enough to compare directly.

Applies to — net10.0, netstandard2.0.

See also — MinHash.Signature, Jaccard.