Image Classification By The Foley-Sammon Transform

Qiu, Tian; Barbero, M.; Gu, Zu-Han; Lee, Sing H.

doi:10.1117/12.7973916

Cited by 72 publications

(25 citation statements)

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“…In the last decade numerous methods have been proposed to solve this problem, Tian et al [9] used the Pseudoinverse method by replacing S À1 W with its pseudoinverse. The Perturbation method is used in [2] and [10], where a small perturbation matrix Á is added to S W in order to make it nonsingular.…”

Section: Introductionmentioning

confidence: 99%

Discriminative common vectors for face recognition

Çevikalp

Neamtu

Wilkes

et al. 2005

IEEE Trans. Pattern Anal. Machine Intell.

480

317

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Abstract-In face recognition tasks, the dimension of the sample space is typically larger than the number of the samples in the training set. As a consequence, the within-class scatter matrix is singular and the Linear Discriminant Analysis (LDA) method cannot be applied directly. This problem is known as the "small sample size" problem. In this paper, we propose a new face recognition method called the Discriminative Common Vector method based on a variation of Fisher's Linear Discriminant Analysis for the small sample size case. Two different algorithms are given to extract the discriminative common vectors representing each person in the training set of the face database. One algorithm uses the within-class scatter matrix of the samples in the training set while the other uses the subspace methods and the Gram-Schmidt orthogonalization procedure to obtain the discriminative common vectors. Then, the discriminative common vectors are used for classification of new faces. The proposed method yields an optimal solution for maximizing the modified Fisher's Linear Discriminant criterion given in the paper. Our test results show that the Discriminative Common Vector method is superior to other methods in terms of recognition accuracy, efficiency, and numerical stability.

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Section: Introductionmentioning

confidence: 99%

Discriminative common vectors for face recognition

Çevikalp

Neamtu

Wilkes

et al. 2005

IEEE Trans. Pattern Anal. Machine Intell.

480

317

View full text Add to dashboard Cite

show abstract

“…A simple and direct attempt is to replace S −1 w with the pseudo-inverse matrix S + w [27]. However, it does not guarantee that Fisher's criterion is still optimized by the largest eigenvectors of S + w S b .…”

Section: Introductionmentioning

confidence: 99%

Efficient and Robust Feature Extraction by Maximum Margin Criterion

Jiang

Zhang

2006

IEEE Trans. Neural Netw.

777

380

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In pattern recognition, feature extraction techniques are widely employed to reduce the dimensionality of data and to enhance the discriminatory information. Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) are two most popular linear dimensionality reduction methods. However, PCA is not very effective for the extraction of the most discriminant features and LDA is not stable due to the small sample size problem. In this paper, we propose some new (linear and nonlinear) feature extractors based on maximum margin criterion (MMC). Geometrically, feature extractors based on MMC maximize the (average) margin between classes after dimensionality reduction. It is shown that MMC can represent class separability better than PCA. As a connection to LDA, we may also derive LDA from MMC by incorporating some constraints. By using some other constraints, we establish a new linear feature extractor that does not suffer from the small sample size problem, which is known to cause serious stability problems for LDA. The kernelized (nonlinear) counterpart of this linear feature extractor is also established in the paper. Our extensive experiments demonstrate that the new feature extractors are effective, stable, and efficient.

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“…In the pseudoinverse method [8] the inverse of within-class scatter matrix S W is estimated by its pseudoinverse and then the conventional eigenvalue problem is solved to compute the orientation matrix W. The pseudoinverse method implemented in this paper is described as follows:…”

Section: Pseudoinverse Methodsmentioning

confidence: 99%

“…Since the null LDA technique discards the range space of S W , it throws away some important information useful for classification. The other technique is the pseudoinverse technique [8] which avoids the singularity problem but discards the null space of S W . Another way to overcome the singularity problem is through the regularized LDA technique [9], [10] which adds a small positive constant to the eigenvalues of S W to make it non-singular.…”

Section: Introductionmentioning

confidence: 99%