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C-MinHash: Improving Minwise Hashing with Circulant Permutation

ICML 2022 · Learning theory and algorithms › Prediction and decision losses · approach: Locality-sensitive hashing

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
replace K independent permutations with two permutations: initial random σ plus circulant shifts of πMinHash · theory and synthetic data (D=128)estimation variance / MSEHelped
apply initial random permutation σ before circulant hashing (C-MinHash-(σ,π)) instead of none (C-MinHash-(0,π)) (ablation)C-MinHash · BBC, NIPS, MNIST, CIFARMAE of Jaccard estimationHelped
use only one permutation π for both initial shuffle and circulant hashing (C-MinHash-(π,π)) (ablation)C-MinHash-(σ,π) · Words dataset and BBC/NIPS/MNIST/CIFARMSE and MAENo clear effect
circulant shifting without initial permutationMinHash-style circulant hashing · synthetic structured datavariance relative to MinHashMixed
increase K (number of hashes) for C-MinHash-(σ,π)C-MinHash-(σ,π) variance ratio over MinHash · theory, f/D sweepvariance ratio MinHash/C-MinHashHelped

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