Formulating face verification with semidefinite programming

Shuicheng Yan, Jianzhuang Liu, Xiaoou Tang, Thomas S. Huang

Research output: Contribution to journalArticlepeer-review


This paper presents a unified solution to three unsolved problems existing in face verification with subspace learning techniques: selection of verification threshold, automatic determination of subspace dimension, and deducing feature fusing weights. In contrast to previous algorithms which search for the projection matrix directly, our new algorithm investigates a similarity metric matrix (SMM). With a certain verification threshold, this matrix is learned by a semidefinite programming approach, along with the constraints of the kindred pairs with similarity larger than the threshold, and inhomogeneous pairs with similarity smaller than the threshold. Then, the subspace dimension and the feature fusing weights are simultaneously inferred from the singular value decomposition of the derived SMM. In addition, the weighted and tensor extensions are proposed to further improve the algorithmic effectiveness and efficiency, respectively. Essentially, the verification is conducted within an affine subspace in this new algorithm and is, hence, called the affine subspace for verification (ASV). Extensive experiments show that the ASV can achieve encouraging face verification accuracy in comparison to other subspace algorithms, even without the need to explore any parameters.

Original languageEnglish (US)
Pages (from-to)2802-2810
Number of pages9
JournalIEEE Transactions on Image Processing
Issue number11
StatePublished - Nov 2007


  • Dimensionality reduction
  • Face verification
  • Subspace dimension determination
  • Threshold determination

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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