Binary Hashing with Semidefinite Relaxation and Augmented Lagrangian

  • Thanh-Toan DoEmail author
  • Anh-Dzung Doan
  • Duc-Thanh Nguyen
  • Ngai-Man Cheung
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9906)


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.


Two-step hashing Semidefinite programming Augmented Lagrangian 


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Thanh-Toan Do
    • 1
    Email author
  • Anh-Dzung Doan
    • 1
  • Duc-Thanh Nguyen
    • 1
  • Ngai-Man Cheung
    • 1
  1. 1.Singapore University of Technology and DesignSingaporeSingapore

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