Complementary Projection Hashing

Recently, hashing techniques have been widely applied to solve the approximate nearest neighbors search problem in many vision applications. Generally, these hashing approaches generate 2ᶜ buckets, where c is the length of the hash code. A good hashing method should satisfy the following two requirements: 1) mapping the nearby data points into the same bucket or nearby (measured by the Hamming distance) buckets. 2) all the data points are evenly distributed among all the buckets. In this paper, we propose a novel algorithm named Complementary Projection Hashing (CPH) to find the optimal hashing functions which explicitly considers the above two requirements. Specifically, CPH aims at sequentially finding a series of hyper planes (hashing functions) which cross the sparse region of the data. At the same time, the data points are evenly distributed in the hyper cubes generated by these hyper planes. The experiments comparing with the state-of-the-art hashing methods demonstrate the effectiveness of the proposed method.