Extended Min-Hash Focusing On Intersection Cardinality

Min-Hash is a reputable hashing technique which realizes set similarity search. Min-Hash assumes the Jaccard similarity vertical bar A boolean AND B vertical bar/vertical bar A boolean OR B vertical bar as the similarity measure between two sets A and B. Accordingly, Min-Hash is not optimal for applications which would like to measure the set similarity with the intersection cardinality vertical bar A boolean AND B vertical bar, since the Jaccard similarity decreases irrespective of vertical bar A boolean AND B vertical bar, as the gap between vertical bar A vertical bar and vertical bar B vertical bar becomes larger. This paper shows that, by modifying Min-Hash slightly, we can effectively settle the above difficulty inherent to Min-Hash. Our method is shown to be valid both by theoretical analysis and with experiments.