• Corpus ID: 17740457

Characterization of a Family of Algorithms for Generalized Discriminant Analysis on Undersampled Problems

@article{Ye2005CharacterizationOA,
  title={Characterization of a Family of Algorithms for Generalized Discriminant Analysis on Undersampled Problems},
  author={Jieping Ye},
  journal={J. Mach. Learn. Res.},
  year={2005},
  volume={6},
  pages={483-502}
}
  • Jieping Ye
  • Published 1 December 2005
  • Computer Science
  • J. Mach. Learn. Res.
A generalized discriminant analysis based on a new optimization criterion is presented. The criterion extends the optimization criteria of the classical Linear Discriminant Analysis (LDA) when the scatter matrices are singular. An efficient algorithm for the new optimization problem is presented.The solutions to the proposed criterion form a family of algorithms for generalized LDA, which can be characterized in a closed form. We study two specific algorithms, namely Uncorrelated LDA (ULDA) and… 

Figures and Tables from this paper

Kernel Uncorrelated and Orthogonal Discriminant Analysis: A Unified Approach

The experimental results show that both KUDA and KODA are very competitive in comparison with other nonlinear discriminant algorithms in terms of classification accuracy.

A unified framework for generalized Linear Discriminant Analysis

  • Shuiwang JiJieping Ye
  • Computer Science
    2008 IEEE Conference on Computer Vision and Pattern Recognition
  • 2008
A unified framework for generalized LDA is proposed via a transfer function, which elucidates the properties of various algorithms and their relationships and proposes an efficient model selection algorithm for LDA.

On sparse linear discriminant analysis algorithm for high‐dimensional data classification

In this paper, a sparse linear discriminant analysis (LDA) algorithm for high‐dimensional objects in subspaces is presented and an iterative algorithm for computing such sparse and orthogonal vectors in the LDA is developed.

Generalized Linear Discriminant Analysis: A Unified Framework and Efficient Model Selection

A unified framework for generalized LDA is proposed, which elucidates the properties of various algorithms and their relationships, and shows that the matrix computations involved in LDA-based algorithms can be simplified so that the cross-validation procedure for model selection can be performed efficiently.

Fisher Discriminant Analysis With L1-Norm

A new method is proposed, termed LDA-L1, by maximizing the ratio of the between- class dispersion to the within-class dispersion using the L1-norm rather than the L2-norm, which is robust to outliers, and is solved by an iterative algorithm proposed.

Characterization of All Solutions for Undersampled Uncorrelated Linear Discriminant Analysis Problems

The uncorrelated linear discriminant analysis for undersampled problems is studied and it is proved that the optimal solutions are exactly the solutions of the corresponding optimization problem with minimum Frobenius norm.

A Direct Kernel Uncorrelated Discriminant Analysis Algorithm

Experimental results show that the proposed method is very competitive in comparison with some existing discriminant analysis algorithms, in terms of recognition rate and robustness with respect to kernel parameters.

SRDA: An Efficient Algorithm for Large-Scale Discriminant Analysis

By using spectral graph analysis, SRDA casts discriminant analysis into a regression framework that facilitates both efficient computation and the use of regularization techniques, and there is no eigenvector computation involved, which is a huge save of both time and memory.

Feature Reduction via Generalized Uncorrelated Linear Discriminant Analysis

An algorithm called ULDA/QR is proposed, based on a novel optimization criterion, to address the singularity problem which occurs in undersampled problems, where the data dimension is larger than the sample size.

Sparse Uncorrelated Linear Discriminant Analysis for Undersampled Problems

This paper proposes a new model for sparse uncorrelated LDA (ULDA), based on the characterization of all solutions of the generalized ULDA, which incorporates sparsity into the ULDA transformation by seeking the solution with minimum ℓ1-norm from all minimum dimension solutions.
...

References

SHOWING 1-10 OF 47 REFERENCES

An optimization criterion for generalized discriminant analysis on undersampled problems

An optimization criterion is presented for discriminant analysis that extends the optimization criteria of the classical Linear Discriminant Analysis through the use of the pseudoinverse when the scatter matrices are singular, overcoming a limitation of classical LDA.

An Optimal Transformation for Discriminant and Principal Component Analysis

It is shown that the method proposed is better than the classical method for L classes and is a generalization of the optimal set of discriminant vectors proposed for two-class problems.

Generalized Discriminant Analysis Using a Kernel Approach

A new method that is close to the support vector machines insofar as the GDA method provides a mapping of the input vectors into high-dimensional feature space to deal with nonlinear discriminant analysis using kernel function operator.

Feature extraction via generalized uncorrelated linear discriminant analysis

The proposed ULDA/GSVD algorithm is applicable for undersampled problem, where the data dimension is much larger than the data size, such as text and image retrieval, and the solution is shown to be independent of the amount of perturbation applied.

An Optimal Set of Discriminant Vectors

A new method for the extraction of features in a two-class pattern recognition problem is derived that is based entirely upon discrimination or separability as opposed to the more common approach of fitting.

Penalized Discriminant Analysis

A penalized version of Fisher's linear discriminant analysis is described, designed for situations in which there are many highly correlated predictors, such as those obtained by discretizing a function, or the grey-scale values of the pixels in a series of images.

Dual-space linear discriminant analysis for face recognition

  • Xiaogang WangXiaoou Tang
  • Computer Science
    Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004.
  • 2004
A dual-space LDA approach for face recognition is proposed to take full advantage of the discriminative information in the face space and outperforms existing LDA approaches.