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Discriminant Analysis on Embedded Manifold

  • Shuicheng Yan
  • Hongjiang Zhang
  • Yuxiao Hu
  • Benyu Zhang
  • Qiansheng Cheng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3021)

Abstract

Previous manifold learning algorithms mainly focus on uncovering the low dimensional geometry structure from a set of samples that lie on or nearly on a manifold in an unsupervised manner. However, the representations from unsupervised learning are not always optimal in discriminating capability. In this paper, a novel algorithm is introduced to conduct discriminant analysis in term of the embedded manifold structure. We propose a novel clustering algorithm, called Intra-Cluster Balanced K-Means (ICBKM), which ensures that there are balanced samples for the classes in a cluster; and the local discriminative features for all clusters are simultaneously calculated by following the global Fisher criterion. Compared to the traditional linear/kernel discriminant analysis algorithms, ours has the following characteristics: 1) it is approximately a locally linear yet globally nonlinear discriminant analyzer; 2) it can be considered a special Kernel-DA with geometry-adaptive-kernel, in contrast to traditional KDA whose kernel is independent to the samples; and 3) its computation and memory cost are reduced a great deal compared to traditional KDA, especially for the cases with large number of samples. It does not need to store the original samples for computing the low dimensional representation for new data. The evaluation on toy problem shows that it is effective in deriving discriminative representations for the problem with nonlinear classification hyperplane. When applied to the face recognition problem, it is shown that, compared with LDA and traditional KDA on YALE and PIE databases, the proposed algorithm significantly outperforms LDA and

Keywords

Discriminant Analysis Face Recognition Near Neighbor Locality Preserve Projection Nonlinear Dimensionality Reduction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Shuicheng Yan
    • 2
  • Hongjiang Zhang
    • 1
  • Yuxiao Hu
    • 1
  • Benyu Zhang
    • 1
  • Qiansheng Cheng
    • 2
  1. 1.Microsoft Research AsiaBeijingP.R.China
  2. 2.School of Mathematical SciencesPeking UniversityBeijingP.R. China

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