## Discriminant analysis based on Kernelized Decision Boundary for Face Recognition

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### BibTeX

@MISC{Zhang_discriminantanalysis,

author = {Baochang Zhang and Xilin Chen},

title = {Discriminant analysis based on Kernelized Decision Boundary for Face Recognition},

year = {}

}

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### Abstract

Abstract. A novel nonlinear discriminant analysis method, Kernelized Decision Boundary Analysis (KDBA), is proposed in our paper, whose Decision Boundary feature vectors are the normal vector of the optimal Decision Boundary in terms of the Structure Risk Minimization principle. We also use a simple method to prove a property of Support Vector Machine (SVM) algorithm, which is combined with the optimal Decision Boundary Feature matrix to make our method consistent with the Kernel Fisher method(KFD). Moreover, KDBA is easily used in its applications, and the traditional Decision Boundary Analysis implementations are computationally expensive and sensitive to the size of the problem. Text classification problem is first used to testify the effectiveness of KDBA. Then experiments on the large-scale face database, the CAS-PEAL database, have illustrated its excellent performance compared with some popular face recognition methods such as Eigenface, Fisherface, and KFD.

### Citations

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(Show Context)
Citation Context ...ion and density estimation. SVM is a general algorithm based on guaranteed risk bounds of statistical learning, the so-called structural risk minimization principle. And we can refer to the tutorials =-=[11]-=- about the SVM. The success of SVM in face recognition [12, 13] as a recognizer provides us with further motivations to utilize SVM to enhance the performance of our system. However, we did not constr... |

1207 | Nonlinear component analysis as a kernel eigenvalue problem
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Citation Context ...e the complex nonlinear variations in the training dataset. In recent years, the kernelized feature extraction methods have been paid much attention, such as Kernel Principal Component Analysis (KPCA)=-=[1]-=- and Kernel Fisher Discriminant analysis (KFD) [1,2,3], which are well-known nonlinear extensions to PCA and FDA respectively. However, the KFD cannot be easily used in real applications. The reason i... |

376 | Fisher discriminant analysis with kernels
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Citation Context ... dataset. In recent years, the kernelized feature extraction methods have been paid much attention, such as Kernel Principal Component Analysis (KPCA)[1] and Kernel Fisher Discriminant analysis (KFD) =-=[1,2,3]-=-, which are well-known nonlinear extensions to PCA and FDA respectively. However, the KFD cannot be easily used in real applications. The reason is that the projection directions of KFD often lie in t... |

246 | Generalized discriminant analysis using a kernel approach
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(Show Context)
Citation Context ... dataset. In recent years, the kernelized feature extraction methods have been paid much attention, such as Kernel Principal Component Analysis (KPCA)[1] and Kernel Fisher Discriminant analysis (KFD) =-=[1,2,3]-=-, which are well-known nonlinear extensions to PCA and FDA respectively. However, the KFD cannot be easily used in real applications. The reason is that the projection directions of KFD often lie in t... |

209 | Gabor feature based classification using the enhanced Fisher linear discriminant model for face recognition
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(Show Context)
Citation Context ... face recognition schemes, such as Eigenface, Fisherface, GKFD, and so on. Gabor wavelet feature has been combined with some discriminant methods and successfully used in the face recognition problem =-=[16, 17]-=-. Therefore, we try to make full use of Gabor wavelet representation of face images before using KDBA to get the transformation matrix. 7. Acknowledgement This research is partially sponsored by Natur... |

166 |
and Anil K Jain, Handbook of face recognition
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(Show Context)
Citation Context ...KDBA, whichsis easily realized in its application. In section 5, we will give some experiment resultsson the Text classification problem and face recognition in the large-scale CAS-PEALsface database =-=[14,18]-=-. In the last section, we will make some conclusions about thesproposed method.s2sKernel Fisher Discriminant AnalysissWe first describe, in this paper, the Kernel Fisher analysis method, which is a we... |

75 | Face Recognition by Support Vector Machines
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Citation Context ...d on guaranteed risk bounds of statistical learning, the so-called structural risk minimization principle. And we can refer to the tutorials [11] about the SVM. The success of SVM in face recognition =-=[12, 13]-=- as a recognizer provides us with further motivations to utilize SVM to enhance the performance of our system. However, we did not construct SVM classifier, and just used it to find the support vector... |

70 |
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Citation Context ...). The algorithm tries to extract the necessarysfeature vectors to achieve the same classification accuracy as in the original space. The decision boundary theory was first proposed by Fukunaga et al =-=[6, 7]-=- and further developed by Lee [8] et al. However, the existing implementations of calculating the Decision Boundary Feature Matrix are computationally expensive and sensitive to the sample size. Moreo... |

59 | Feature extraction based on decision boundaries
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Citation Context ...e necessarysfeature vectors to achieve the same classification accuracy as in the original space. The decision boundary theory was first proposed by Fukunaga et al [6, 7] and further developed by Lee =-=[8]-=- et al. However, the existing implementations of calculating the Decision Boundary Feature Matrix are computationally expensive and sensitive to the sample size. Moreover, the decision boundary method... |

50 | Enhanced Fisher Linear Discriminant Models for Face Recognition
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Citation Context ...1 61 58.7 62.4 63.1 64 Aging 50 72.7 77.3 84.8 87.9 87.9 Distance 74.2 93.5 94.9 96 96 96 Expression 53.7 71.3 78.2 78.2 78.5 79.9 Backgroun 80.5 d 94.4 91.7 94.1 94.3 94.4 Fisherface method refers to=-=[15]-=- From above experiments, the KDBA method has achieved better performance than other popular face recognition schemes. The Kernelized Decision Boundary Feature vector can be thought of as the optimal d... |

48 |
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Citation Context ...d on guaranteed risk bounds of statistical learning, the so-called structural risk minimization principle. And we can refer to the tutorials [11] about the SVM. The success of SVM in face recognition =-=[12, 13]-=- as a recognizer provides us with further motivations to utilize SVM to enhance the performance of our system. However, we did not construct SVM classifier, and just used it to find the support vector... |

40 |
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Citation Context ...o perform FDA in a higher dimensional space F , it is equal to maximize Eq.4. T w Sbw tr( Sb) J( w) = = . (4) T w Sww tr( Sw) Because any solution w ∈ F should lie in the span of all the samples in F =-=[9,10]-=-, there exists: i i i isn w = ∑ α i φ ( xi ) , α i, i = 1, 2... n. , (5) i= 1 Then we will get the following Maximizing Criterion: T α K b α J ( α ) = , (6) T α K w α where w K and K b are defined as ... |

34 |
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(Show Context)
Citation Context ...e, when the input space is mapped to a feature space through a kernel function. As a result, the scatter matrices become singular, which is the so-called “Small Sample Size problem” (SSS). Similar to =-=[5]-=-, KFD simply adds a perturbation to within-class scatter matrix. Of course, it has the same stability problem as that in [5], because eigenvectors are sensitive to the small perturbation, moreover, th... |

8 |
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(Show Context)
Citation Context ...inear extensions to PCA and FDA respectively. However, the KFD cannot be easily used in real applications. The reason is that the projection directions of KFD often lie in the span of all the samples =-=[4]-=-, therefore, the dimension of the feature often becomes very large, when the input space is mapped to a feature space through a kernel function. As a result, the scatter matrices become singular, whic... |

8 |
De Prins, "SVM-based Nonparametric Discriminant Analysis, An application to Face Detection
- Fransens
(Show Context)
Citation Context ...1 nix i n i ii == ∑ = αw φα , (5)sThen we will get the following Maximizing Criterion:sαKα αKαα w T b T J =)(s, (6)swhere wKsand bKsare defined as following:s∑ = −−= C i T ijijiw mmEp 1 ))(()( ηηϖKs, =-=(7)-=-s∑ = −−= C i T iiib mmmmp 1 __ ))()((ϖK , (8)swheresTjnjjj xxkxxkxxk )),(),...,,(),,(( 21=η ,s = ∑∑∑ === iii n j jn i n j j i n j j i i xxkn xxk n xxk n m 11 21 1 ),(1,..,),(1,),(1 , ands... |

6 | Discriminant Gaborfaces and Support Vector Machines Classifier for Face Recognition
- Zhang, Gao, et al.
- 2004
(Show Context)
Citation Context ... face recognition schemes, such as Eigenface, Fisherface, GKFD, and so on. Gabor wavelet feature has been combined with some discriminant methods and successfully used in the face recognition problem =-=[16, 17]-=-. Therefore, we try to make full use of Gabor wavelet representation of face images before using KDBA to get the transformation matrix. 7. Acknowledgement This research is partially sponsored by Natur... |

4 |
The CAS-PEAL Large-Scale Face Database and Evaluation Protocols
- Gao, Cao, et al.
- 2004
(Show Context)
Citation Context ...KDBA, which is easily realized in its application. In section 5, we will give some experiment results on the Text classification problem and face recognition in the large-scale CAS-PEAL face database =-=[14,18]-=-. In the last section, we will make some conclusions about the proposed method. 2. Kernel Fisher Discriminant Analysis We first describe, in this paper, the Kernel Fisher analysis method, which is a w... |

3 |
Null space based Kernel Fisher Discriminant analysis for face recognition
- Liu, Wang
- 2004
(Show Context)
Citation Context ...o perform FDA in a higher dimensional space F , it is equal to maximize Eq.4. T w Sbw tr( Sb) J( w) = = . (4) T w Sww tr( Sw) Because any solution w ∈ F should lie in the span of all the samples in F =-=[9,10]-=-, there exists: i i i isn w = ∑ α i φ ( xi ) , α i, i = 1, 2... n. , (5) i= 1 Then we will get the following Maximizing Criterion: T α K b α J ( α ) = , (6) T α K w α where w K and K b are defined as ... |

1 |
De Prins, "SVM-based Nonparametric Discriminant Analysis, An application to Face Detection
- Fransens
(Show Context)
Citation Context ...). The algorithm tries to extract the necessarysfeature vectors to achieve the same classification accuracy as in the original space. The decision boundary theory was first proposed by Fukunaga et al =-=[6, 7]-=- and further developed by Lee [8] et al. However, the existing implementations of calculating the Decision Boundary Feature Matrix are computationally expensive and sensitive to the sample size. Moreo... |

1 |
Jain (Eds). "Handbook of Face Recognition
- Li, Anil
(Show Context)
Citation Context ...KDBA, which is easily realized in its application. In section 5, we will give some experiment results on the Text classification problem and face recognition in the large-scale CAS-PEAL face database =-=[14,18]-=-. In the last section, we will make some conclusions about the proposed method. 2. Kernel Fisher Discriminant Analysis We first describe, in this paper, the Kernel Fisher analysis method, which is a w... |