Generalizing discriminant analysis using the generalized singular value decomposition

Howland, Peg; Park, H.

doi:10.1109/tpami.2004.46

Cited by 323 publications

(179 citation statements)

References 14 publications

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“…We study theoretical and algorithmic relationships among several generalized LDA algorithms and compare their computational complexities and performances. Computationally efficient algorithm is also proposed which computes the exactly same solution as that in [4,10] but saves computational complexities greatly. In Section 3, nonlinear extensions of these generalized LDA algorithms are presented.…”

Section: (S T ) Let Us Denote a Data Set A Asmentioning

confidence: 99%

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A comparison of generalized linear discriminant analysis algorithms

Park¹,

Park

2008

Pattern Recognition

146

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Linear Discriminant Analysis (LDA) is a dimension reduction method which finds an optimal linear transformation that maximizes the class separability. However, in undersampled problems where the number of data samples is smaller than the dimension of data space, it is difficult to apply the LDA due to the singularity of scatter matrices caused by high dimensionality. In order to make the LDA applicable, several generalizations of the LDA have been proposed recently. In this paper, we present theoretical and algorithmic relationships among several generalized LDA algorithms and compare their computational complexities and performances in text classification and face recognition. Towards a practical dimension reduction method for high dimensional data, an efficient algorithm is proposed, Preprint submitted to Elsevier Science 27 June 2007 which reduces the computational complexity greatly while achieving competitive prediction accuracies. We also present nonlinear extensions of these LDA algorithms based on kernel methods. It is shown that a generalized eigenvalue problem can be formulated in the kernel-based feature space, and generalized LDA algorithms are applied to solve the generalized eigenvalue problem, resulting in nonlinear discriminant analysis. Performances of these linear and nonlinear discriminant analysis algorithms are compared extensively.

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Section: (S T ) Let Us Denote a Data Set A Asmentioning

confidence: 99%

“…Howland et al [4,10] applied the Generalized Singular Value Decomposition (GSVD) due to Paige and Saunders [11] to overcome the limitation of the classical LDA.…”

Section: Lda Based On the Generalized Singular Value Decompositionmentioning

confidence: 99%

A comparison of generalized linear discriminant analysis algorithms

Park¹,

Park

2008

Pattern Recognition

146

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“…Recently, a method called LDA/GSVD has been developed which is a generalization of LDA based on the generalized singular value decomposition (GSVD) [16,17]. By using the generalized singular value decomposition (GSVD), LDA/GSVD solves a generalized eigenvalue problem…”

Section: Kernel Discriminant Analysis Based On Generalized Singular Vmentioning

confidence: 99%

Fingerprint classification using fast Fourier transform and nonlinear discriminant analysis

Park

2005

Pattern Recognition

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In this paper, we present a new approach for fingerprint classification based on Discrete Fourier Transform (DFT) and nonlinear discriminant analysis. Utilizing the Discrete Fourier Transform and directional filters, a reliable and efficient directional image is constructed from each fingerprint image, and then nonlinear discriminant analysis is applied to the constructed directional images, reducing the dimension dramatically and extracting the discriminant features. The proposed method explores the capability of DFT and directional filtering in dealing with low quality images and the effectiveness of nonlinear feature extraction method in fingerprint classification. Experimental results demonstrates competitive performance compared with other published results.

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“…The basic idea of this method is to first use principal component analysis (PCA) Dimension reduction, eliminate the singularity, and then use the linear discriminant analysis method to classify.In addition to this, some scholars have proposed an LDA/GSVD algorithm to solve the singularity problem of w S [3] . The algorithm avoids the direct inversion of w S in the classical LDA algorithm by generalized singular value decomposition.…”

Section: Introductionmentioning

confidence: 99%

A new method for human ear recognition using Haar wavelet decomposition and LDA/GSVD

Zhao¹

2018

Proceedings of the 2018 8th International Conference on Manufacturing Science and Engineering (ICMSE 2018)

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Abstract. In the case of high dimension and small sample, the feature extraction method using Fisher linear discriminant analysis has a problem of pathological singularity. There are many solutions to this problem, in which LDA/GSVD algorithm overcomes the shortcomings of the existing methods, has a good recognition rate. However, the direct use of LDA/GSVD to reduce the dimension of human ear images, it still encounters the problem of large amount of calculation and slow calculation speed. So the author proposes a new method which apply wavelet decomposition on the human ear image and then use LDA/GSVD algorithm. The method is proved by experiments that it has a good recognition rate and is an effective feature extraction approach.

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Generalizing discriminant analysis using the generalized singular value decomposition

Cited by 323 publications

References 14 publications

A comparison of generalized linear discriminant analysis algorithms

A comparison of generalized linear discriminant analysis algorithms

Fingerprint classification using fast Fourier transform and nonlinear discriminant analysis

A new method for human ear recognition using Haar wavelet decomposition and LDA/GSVD

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