A new robust quadratic discriminant function

Sakai, Mitsuru; Yoneda, Masaaki; Häse, H.

doi:10.1109/icpr.1998.711089

Cited by 10 publications

(8 citation statements)

References 5 publications

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“…Since the RQDF depends on linear transformation of the coordinate system, the dependence should be investigated in the future. If a learning sample size is quite close to the dimensionality of the features, the performance of our RQDF is inadequate compared with the MQDF or k-NN [14,16]. Therefore, it appears that there remain other factors that affect the performance of the quadratic discriminant function.…”

Section: Discussionmentioning

confidence: 98%

“…(16), where l 1 l 2 2. 3 In this figure, it is seen that linear relation (16) can be used to rectify sample eigenvalues if l 2 is smaller than 0.75. If l 2 is greater than 0.75, however, applying Eq.…”

Section: Simultaneous Linear Equations To Approximate Expected Samplementioning

confidence: 93%

“…We derive their approximate equations in Section 3. In the two-dimensional case, however, their relations are exactly evaluated from the Wishart distribution [12]. Some examples of the relations are shown in Fig.…”

Section: Rectification Of Sample Eigenvaluementioning

confidence: 99%

“…Eqs. (16) and (17) are used. The occurrence probabilities of both classes c j j 1, 2 are equal, that is, P 1 P 2 in this section.…”

Section: Recognition Experimentsmentioning

confidence: 99%

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A quadratic discriminant function based on bias rectification of eigenvalues

et al. 2000

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We propose a new quadratic discriminant function. First, we show that the eigenvalues of a covariance matrix obtained from samples are biased. Then, we describe how to rectify them and how to use the rectified eigenvalues. In order to derive the relation between sample eigenvalues and true eigenvalues, we analyze the biases of the expected sample eigenvalues by using the perturbation method and obtain approximate simultaneous linear equations to rectify sample eigenvalues in multidimensional normal cases. Finally, we show by a Monte Carlo method that our discriminant function works effectively in eight-dimensional normal cases especially in the case of a small sample size.

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Section: Discussionmentioning

confidence: 98%

Section: Simultaneous Linear Equations To Approximate Expected Samplementioning

confidence: 93%

Section: Rectification Of Sample Eigenvaluementioning

confidence: 99%

“…Eqs. (16) and (17) are used. The occurrence probabilities of both classes c j j 1, 2 are equal, that is, P 1 P 2 in this section.…”

Section: Recognition Experimentsmentioning

confidence: 99%

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A quadratic discriminant function based on bias rectification of eigenvalues

et al. 2000

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“…In the case of recognizing character patterns, it is known that the Mahalanobis distance has disadvantages. One big disadvantage is caused by small number of samples [19], [20], [21]. To decrease this influence, many regularization methods of discriminant functions are proposed [4], [5].…”

Section: A Discriminant Functionmentioning

confidence: 99%

A noise-adaptive discriminant function and its application to blurred machine-printed Kanji recognition

Omachi

Sun

Aso

2000

IEEE Trans. Pattern Anal. Machine Intell.

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Accurate recognition of blurred images is a practical but hitherto mostly overlooked problem. In this paper, we quantify the level of noise in blurred images and propose a new modification of discriminant functions that adaps to the level of noise. Experimental results indicate that the proposed method actually enhances the existing statistical methods, and has impressive ability to recognize blurred image patterns.

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A Method to Estimate the True Mahalanobis Distance from Eigenvectors of Sample Covariance Matrix

Omachi

Aso

2002

Lecture Notes in Computer Science

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In statistical pattern recognition, the parameters of distributions are usually estimated from training sample vectors. However, estimated parameters contain estimation errors, and the errors cause bad influence on recognition performance when the sample size is not sufficient. Some methods can obtain better estimates of the eigenvalues of the true covariance matrix and can avoid bad influences caused by estimation errors of eigenvalues. However, estimation errors of eigenvectors of covariance matrix have not been considered enough. In this paper, we consider estimation errors of eigenvectors and show the errors can be regarded as estimation errors of eigenvalues. Then, we present a method to estimate the true Mahalanobis distance from eigenvectors of the sample covariance matrix. Recognition experiments show that by applying the proposed method, the true Mahalanobis distance can be estimated even if the sample size is small, and better recognition accuracy is achieved. The proposed method is useful for the practical applications of pattern recognition since the proposed method is effective without any hyper-parameters.

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A new robust quadratic discriminant function

Cited by 10 publications

References 5 publications

A quadratic discriminant function based on bias rectification of eigenvalues

A quadratic discriminant function based on bias rectification of eigenvalues

A noise-adaptive discriminant function and its application to blurred machine-printed Kanji recognition

A Method to Estimate the True Mahalanobis Distance from Eigenvectors of Sample Covariance Matrix

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