Binary Hashing with Semidefinite Relaxation and Augmented Lagrangian

TL;DR

This paper introduces two novel methods for binary code inference in hashing, utilizing semidefinite relaxation and augmented Lagrangian techniques, achieving competitive results on benchmark datasets.

Contribution

It presents a unified formulation for supervised and unsupervised hashing and proposes two new algorithms for solving binary quadratic problems efficiently.

Findings

Semidefinite relaxation achieves a globally optimal solution.

Augmented Lagrangian approach directly solves BQP without relaxation.

Proposed methods outperform state-of-the-art on benchmark datasets.

Abstract

This paper proposes two approaches for inferencing binary codes in two-step (supervised, unsupervised) hashing. We first introduce an unified formulation for both supervised and unsupervised hashing. Then, we cast the learning of one bit as a Binary Quadratic Problem (BQP). We propose two approaches to solve BQP. In the first approach, we relax BQP as a semidefinite programming problem which its global optimum can be achieved. We theoretically prove that the objective value of the binary solution achieved by this approach is well bounded. In the second approach, we propose an augmented Lagrangian based approach to solve BQP directly without relaxing the binary constraint. Experimental results on three benchmark datasets show that our proposed methods compare favorably with the state of the art.