Distributed Discrete Hashing by Equivalent Continuous Formulation

Hashing based approximate nearest neighbor search has attracted considerable attention in various fields. Most of the existing hashing methods are centralized, which cannot be used for many large-scale applications with the data stored or collected in a distributed manner. In this article, we consider the distributed hashing problem. The main difficulty of hashing is brought by its inherent binary constraints, which makes the problem generally NP-hard. Most of the existing distributed hashing methods chose to relax the problem by dropping the binary constraints. However, such a manner will bring additional quantization error, which makes the binary codes less effective. In this paper, we propose a novel distributed discrete hashing method, which learns effective hash codes without using any relaxations. Specifically, we give a method to transform the discrete hashing problem into an equivalent distributed continuous optimization problem. After transformation, we devise a distributed discrete hashing (dDH) algorithm based on the idea of DC programming to solve the problem. To obtain more efficient hash codes, we further add bits balance and uncorrelation constraints to the hashing problem, and we also propose a distributed constrained discrete hashing algorithm (dCDH) to solve this problem. Extensive experiments are provided to show the superiority of the proposed methods.