  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
problem. The new scheme utilizes asymmetric transformations to cancel the bias
of traditional minhash 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 high-dimensional datasets validate our
claims and 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.
