DartMinHash: Fast Sketching for Weighted Sets
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Weighted minwise hashing is a standard dimensionality reduction technique with applications to similarity search and large-scale kernel machines. We introduce a simple algorithm that takes a weighted set x ∈ℝ_≥ 0^d and computes k independent minhashes in expected time O(k log k + ‖ x ‖_0log( ‖ x ‖_1 + 1/‖ x ‖_1)), improving upon the state-of-the-art BagMinHash algorithm (KDD '18) and representing the fastest weighted minhash algorithm for sparse data. Our experiments show running times that scale better with k and ‖ x ‖_0 compared to ICWS (ICDM '10) and BagMinhash, obtaining 10x speedups in common use cases. Our approach also gives rise to a technique for computing fully independent locality-sensitive hash values for (L, K)-parameterized approximate near neighbor search under weighted Jaccard similarity in optimal expected time O(LK + ‖ x ‖_0), improving on prior work even in the case of unweighted sets.
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