A Scalable Optimization Mechanism for Pairwise Based Discrete Hashing

Maintaining the pairwise relationship among originally high-dimensional data into a low-dimensional binary space is a popular strategy to learn binary codes. One simple and intuitive method is to utilize two identical code matrices produced by hash functions to approximate a pairwise real label matrix. However, the resulting quartic problem in term of hash functions is difficult to directly solve due to the non-convex and non-smooth nature of the objective. In this paper, unlike previous optimization methods using various relaxation strategies, we aim to directly solve the original quartic problem using a novel alternative optimization mechanism to linearize the quartic problem by introducing a linear regression model. Additionally, we find that gradually learning each batch of binary codes in a sequential mode, i.e. batch by batch, is greatly beneficial to the convergence of binary code learning. Based on this significant discovery and the proposed strategy, we introduce a scalable symmetric discrete hashing algorithm that gradually and smoothly updates each batch of binary codes. To further improve the smoothness, we also propose a greedy symmetric discrete hashing algorithm to update each bit of batch binary codes. Moreover, we extend the proposed optimization mechanism to solve the non-convex optimization problems for binary code learning in many other pairwise based hashing algorithms. Extensive experiments on benchmark single-label and multi-label databases demonstrate the superior performance of the proposed mechanism over recent state-of-the-art methods on two kinds of retrieval tasks: similarity and ranking order. The source codes are available on https://github.com/xsshi2015/Scalable-Pairwise-based-Discrete-Hashing.