Discrete Double-bit Hashing

Hashing has been widely used for nearest neighbors search over big data. Hashing encodes high dimensional data points into binary codes. Most hashing methods use the single-bit quantization (SBQ) strategy for coding the data. However, this strategy often encodes neighboring points into totally different bits. Recently, a double-bit quantization (DBQ) strategy was proposed, which can better preserve the similarity of the data. The hashing problems are generally NP-hard, due to the discrete constraints. For tractability, some relaxation methods were proposed by discarding the discrete constraints. However, such a manner makes the hash codes less effective, due to the large quantization error. To obtain high-quality hash codes, some discrete hashing methods were proposed, which directly solve the hashing problem without any relaxations. However, the existing discrete hashing methods can only deal with single-bit hashing. In this paper, we propose a discrete hashing method to solve double-bit hashing problems. To address the difficulty brought by the discrete constraints, we propose a method to transform the discrete hashing problem into an equivalent continuous optimization problem. Then, we devise algorithms based on DC (difference of convex functions) programming to solve the problem. Numerical experiments are provided to show the superiority of the proposed methods.