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 strategy named "re-randomization" in the process of densification that could achieve the smallest variance among all densification schemes. The success of this idea naturally inspires us to generalize one permutation hashing to weighted (non-binary) data, which results in the socalled "bin-wise consistent weighted sampling (BCWS)" algorithm. We analyze the behavior of BCWS and compare it with a recent alternative. Extensive experiments on various datasets illustrates the effectiveness of our proposed methods.

The authors propose that the optimal densification for OPH can actually be further optimized. In usual OPH, we get one permutation of the sparse vector, break the vector into K equal sized bins. In the usual Consistent Weighted Sampling (CWS) approach, we sample non-empty bins from these K bins and retrieve a fixed hash code for these bins. In this new approach, the authors suggest to treat each of the K bins as a separate sparse vector and perform MinHash on these retrieved bins to get a hash code instead of directly getting a Hash code. The authors theoretically prove that this re-randomization achieves the smallest variance among densification schemes(that are used to retrieve hash codes from empty buckets). Also, they extend this idea to weighted non-negative sparse vectors (by a method called Bin-wise CWS) The paper seems to be a subtle improvement over prior work.

Overall the reviewers appreciated the idea, which although incremental, was quite subtle and interesting, and given also the importance of the problem, this was enough for the reviewers to all agree to push this paper over the bar.

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 strategy named "re-randomization" in the process of densification that could achieve the smallest variance among all densification schemes. The success of this idea naturally inspires us to generalize one permutation hashing to weighted (non-binary) data, which results in the socalled "bin-wise consistent weighted sampling (BCWS)" algorithm.

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 strategy named "re-randomization" in the process of densification that could achieve the smallest variance among all densification schemes. The success of this idea naturally inspires us to generalize one permutation hashing to weighted (non-binary) data, which results in the socalled "bin-wise consistent weighted sampling (BCWS)" algorithm.