Multilinear Hyperplane Hashing

Hashing has become an increasingly popular technique for fast nearest neighbor search. Despite its successful progress in classic point-to-point search, there are few studies regarding point-to-hyperplane search, which has strong practical capabilities of scaling up applications like active learning with SVMs. Existing hyperplane hashing methods enable the fast search based on randomly generated hash codes, but still suffer from a low collision probability and thus usually require long codes for a satisfying performance. To overcome this problem, this paper proposes a multilinear hyperplane hashing that generates a hash bit using multiple linear projections. Our theoretical analysis shows that with an even number of random linear projections, the multilinear hash function possesses strong locality sensitivity to hyperplane queries. To leverage its sensitivity to the angle distance, we further introduce an angular quantization based learning framework for compact multilinear hashing, which considerably boosts the search performance with less hash bits. Experiments with applications to large-scale (up to one million) active learning on two datasets demonstrate the overall superiority of the proposed approach.