Jaccard similarity is widely used as a distance measure in many machine learning and search applications. Typically, hashing methods are essential for the use of Jaccard similarity to be practical in large-scale settings. For hashing binary (0/1) data, the idea of one permutation hashing (OPH) with densification significantly accelerates traditional minwise hashing algorithms while providing unbiased and accurate estimates. In this paper, we propose a "re-randomization" strategy in the process of densification and we show that it achieves the smallest variance among existing densification schemes. The success of this idea inspires us to generalize one permutation hashing to weighted (non-binary) data, resulting in the so-called "bin-wise consistent weighted sampling (BCWS)" algorithm. We analyze the behavior of BCWS and compare it with a recent alternative. Experiments on a range of datasets and tasks confirm the effectiveness of proposed methods. We expect that BCWS will be adopted in practice for training kernel machines and fast similarity search.
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