Compressed Hashing

Recent studies have shown that hashing methods are effective for high dimensional nearest neighbor search. A common problem shared by many existing hashing methods is that in order to achieve a satisfied performance, a large number of hash tables (i.e., long codewords) are required. To address this challenge, in this paper we propose a novel approach called Compressed Hashing by exploring the techniques of sparse coding and compressed sensing. In particular, we introduce a sparse coding scheme, based on the approximation theory of integral operator, that generate sparse representation for high dimensional vectors. We then project sparse codes into a low dimensional space by effectively exploring the Restricted Isometry Property (RIP), a key property in compressed sensing theory. Both of the theoretical analysis and the empirical studies on two large data sets show that the proposed approach is more effective than the state-of-the-art hashing algorithms.