Asymmetric minwise hashing for indexing binary inner products and set containment

Minwise hashing (Minhash) is a widely popular indexing scheme in practice. Minhash is designed for estimating set resemblance and is known to be suboptimal in many applications where the desired measure is set overlap (i.e., inner product between binary vectors) or set containment. Minhash has inherent bias towards smaller sets, which adversely affects its performance in applications where such a penalization is not desirable. In this paper, we propose asymmetric minwise hashing (MH-ALSH), to provide a solution to this well-known problem. The new scheme utilizes asymmetric transformations to cancel the bias of traditionalminhash towards smaller sets, making the final "collision probability" monotonic in the inner product. Our theoretical comparisons show that, for the task of retrieving with binary inner products, asymmetric minhash is provably better than traditional minhash and other recently proposed hashing algorithms for general inner products. Thus, we obtain an algorithmic improvement over existing approaches in the literature. Experimental evaluations on four publicly available highdimensional datasets validate our claims. The proposed scheme outperforms, often significantly, other hashing algorithms on the task of near neighbor retrieval with set containment. Our proposal is simple and easy to implement in practice.