Discriminative Locality Alignment

  • Authors:
  • Tianhao Zhang;Dacheng Tao;Jie Yang

  • Affiliations:
  • Institute of Image Processing and Pattern Recognition, Shanghai Jiao Tong University, Shanghai, China;School of Computer Engineering, Nanyang Technological University, Singapore and College of Computer Science, Zhejiang University, China;Institute of Image Processing and Pattern Recognition, Shanghai Jiao Tong University, Shanghai, China

  • Venue:
  • ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
  • Year:
  • 2008

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Abstract

Fisher's linear discriminant analysis (LDA), one of the most popular dimensionality reduction algorithms for classification, has three particular problems: it fails to find the nonlinear structure hidden in the high dimensional data; it assumes all samples contribute equivalently to reduce dimension for classification; and it suffers from the matrix singularity problem. In this paper, we propose a new algorithm, termed Discriminative Locality Alignment (DLA), to deal with these problems. The algorithm operates in the following three stages: first, in part optimization, discriminative information is imposed over patches, each of which is associated with one sample and its neighbors; then, in sample weighting, each part optimization is weighted by the margin degree, a measure of the importance of a given sample; and finally, in whole alignment, the alignment trick is used to align all weighted part optimizations to the whole optimization. Furthermore, DLA is extended to the semi-supervised case, i.e., semi-supervised DLA (SDLA), which utilizes unlabeled samples to improve the classification performance. Thorough empirical studies on the face recognition demonstrate the effectiveness of both DLA and SDLA.