Improved Densification of One Permutation Hashing

The existing work on densification of one permutation hashing [24] 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 in [24] 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 [24]. 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.