ProbMinHash -- A Class of Locality-Sensitive Hash Algorithms for the (Probability) Jaccard Similarity

TL;DR

This paper introduces a new class of locality-sensitive hash algorithms called ProbMinHash, which significantly speeds up similarity estimation for weighted sets by calculating signature components collectively, improving efficiency and accuracy.

Contribution

It proposes four novel ProbMinHash algorithms that are faster and more accurate than existing methods for probability Jaccard similarity estimation.

Findings

Two algorithms are equivalent to original MinHash but faster.

Two algorithms improve estimation accuracy through statistical dependence.

Specialized algorithms outperform traditional MinHash in efficiency.

Abstract

The probability Jaccard similarity was recently proposed as a natural generalization of the Jaccard similarity to measure the proximity of sets whose elements are associated with relative frequencies or probabilities. In combination with a hash algorithm that maps those weighted sets to compact signatures which allow fast estimation of pairwise similarities, it constitutes a valuable method for big data applications such as near-duplicate detection, nearest neighbor search, or clustering. This paper introduces a class of one-pass locality-sensitive hash algorithms that are orders of magnitude faster than the original approach. The performance gain is achieved by calculating signature components not independently, but collectively. Four different algorithms are proposed based on this idea. Two of them are statistically equivalent to the original approach and can be used as drop-in replacements. The other two may even improve the estimation error by introducing statistical dependence between signature components. Moreover, the presented techniques can be specialized for the conventional Jaccard similarity, resulting in highly efficient algorithms that outperform traditional minwise hashing and that are able to compete with the state of the art.