  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.
