The existing work on densification of one permutation hashing reduces the query processing cost of the $(K,L)$-parameterized Locality Sensitive Hashing (LSH) algorithm with minwise hashing, from $O(dKL)$ to merely $O(d + KL)$, where $d$ is the number of nonzeros of the data vector, $K$ is the number of hashes in each hash table, and $L$ is the number of hash tables. While that is a substantial improvement, our analysis reveals that the existing densification scheme is sub-optimal. In particular, there is no enough randomness in that procedure, which affects its accuracy on very sparse datasets. In this paper, we provide a new densification procedure which is provably better than the existing scheme. This improvement is more significant for very sparse datasets which are common over the web. The improved technique has the same cost of $O(d + KL)$ for query processing, thereby making it strictly preferable over the existing procedure. Experimental evaluations on public datasets, in the task of hashing based near neighbor search, support our theoretical findings.

本文提出了一种新的稠密化策略，使 $(K,L)$ 参数的局部敏感哈希 (Locality Sensitive Hashing)的 minwise 哈希算法在查询处理成本上从 $O(dKL)$ 降至仅 $O(d + KL)$，针对非常稀疏的数据集，该改进的技术表现更好，并且在查询处理成本上与现有程序相同。

一种置换哈希方法的密集性改进