人脸识别技术研究
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摘要
人脸识别技术是计算机模式识别领域非常活跃的研究课题，在法律、商业等领域有着广泛的应用前景。由于人脸图像的特殊性，人脸识别问题也是模式识别领域的一个相当困难的问题，要使这一技术成为完全成熟的技术还有许多工作需要去做。本文结合主成分分析(PCA)人脸识别算法，对其中的部分问题分别进行了深入的研究与探讨，并给出了相应的解决方案。
本文工作包括：
(1)．本文从基于图像整体代数特征PCA算法着手，主要介绍了“特征脸”算法的原理和实现过程，对组成特征投影空间的特征值选择问题，距离度量方法问题及训练样本的选择等进行了一定的研究。主要针对识别准确率，同时兼顾到运算量，本文提出针对不同的样本集，可以综合运算量和识别准确率两个方面，考虑选择不同的特征向量来组成特征空间。同时训练样本的选择也会一定程度上影响识别率。在ORL和Yale人脸数据库上进行的实验也证明了这一点。
(2)．本文针对传统的PCA算法存在的运算量大的缺点，通过对一般的用于人脸识别的小波变换方法加以改进，提出了一种基于小波变换的PCA算法。该算法将小波分解后的细节图像和垂直方向图像结合起来用于PCA的训练识别，取得了优于一般小波方法而与传统PCA算法几乎等同的识别效果，同时，大大减少了PCA算法的运算量，速度提高了6倍多。
(3)．本文针对在每类存在较多样本的情况下，PCA算法无法有效的利用这些样本提高识别率的问题，提出了一种基于独立类别的PCA&SVM的人脸识别算法。该算法通过对每一类别单独使用PCA提取特征子空间后，将投影所得到的特征向量用于构造各类别对应的支持向量机，然后对测试样本进行分类。由于算法对单个类别的多训练样本进行特征提取，因此更为有效的描述了样本的特征空间，同时结合SVM处理高维数据分割的强大能力，取得了很好的识别效果。
The technology of face recognition is an active subject in the area of pattern recognition. There are broad applications in the fields of law, business etc. For the particularity of the face image, face recognition is also the very difficult problem. There is still much work to do. In this paper, some of face recognition algorithms are proposed based on Principle Component Analysis . And the corresponding solutions are given. The work including:
(1) Based on algebraic features of the images, this paper first introduced the PCA-Based face recognition algorithm. Some research have done on the selection of the eigenvector which used to create the eigenspace ,the distance measure methods and the selection of the training set. Considering the recognition performance and the computation time, this paper proposed a method using to select the different number of the eigenvector in allusion to different training datasets. In the end, the ORL and Yale dataset are used for the experiments.
(2) This paper proposed a wavelet transform based recognition algorithm. The computing time of the traditional PCA-Based face recognition algorithm is very large. So the wavelet transform method is used to do the preprocessing. The method this paper proposed is different from the traditional wavelet transform method used in face recognition. In the proposed method, the detail subimage and the vertical direction subimage are combined as the PCA algorithm's training set and the probe image. The experiments results present that the speed of the training and recognition is six times faster than the traditional PCA algorithm introduced in the precious chapter while the correct recognition rate is almost equal to the traditional wavelet transform based face recognition method.
(3) PCA algorithm can't effectively use the training samples to improve the recognition rate while each class has much training samples. This paper proposed a method called PCA&SVM based on each class. After present PCA on each class, their eigenspace are got to train the corresponding Support Vector Machines respectively. Then the probe images are tested by the SVM. Because SVM has the strong ability of segmenting high dimension data and PCA can distill the eigenspace effectively, the result of the experiment is satisfied.
本文工作包括：
(1)．本文从基于图像整体代数特征PCA算法着手，主要介绍了“特征脸”算法的原理和实现过程，对组成特征投影空间的特征值选择问题，距离度量方法问题及训练样本的选择等进行了一定的研究。主要针对识别准确率，同时兼顾到运算量，本文提出针对不同的样本集，可以综合运算量和识别准确率两个方面，考虑选择不同的特征向量来组成特征空间。同时训练样本的选择也会一定程度上影响识别率。在ORL和Yale人脸数据库上进行的实验也证明了这一点。
(2)．本文针对传统的PCA算法存在的运算量大的缺点，通过对一般的用于人脸识别的小波变换方法加以改进，提出了一种基于小波变换的PCA算法。该算法将小波分解后的细节图像和垂直方向图像结合起来用于PCA的训练识别，取得了优于一般小波方法而与传统PCA算法几乎等同的识别效果，同时，大大减少了PCA算法的运算量，速度提高了6倍多。
(3)．本文针对在每类存在较多样本的情况下，PCA算法无法有效的利用这些样本提高识别率的问题，提出了一种基于独立类别的PCA&SVM的人脸识别算法。该算法通过对每一类别单独使用PCA提取特征子空间后，将投影所得到的特征向量用于构造各类别对应的支持向量机，然后对测试样本进行分类。由于算法对单个类别的多训练样本进行特征提取，因此更为有效的描述了样本的特征空间，同时结合SVM处理高维数据分割的强大能力，取得了很好的识别效果。
The technology of face recognition is an active subject in the area of pattern recognition. There are broad applications in the fields of law, business etc. For the particularity of the face image, face recognition is also the very difficult problem. There is still much work to do. In this paper, some of face recognition algorithms are proposed based on Principle Component Analysis . And the corresponding solutions are given. The work including:
(1) Based on algebraic features of the images, this paper first introduced the PCA-Based face recognition algorithm. Some research have done on the selection of the eigenvector which used to create the eigenspace ,the distance measure methods and the selection of the training set. Considering the recognition performance and the computation time, this paper proposed a method using to select the different number of the eigenvector in allusion to different training datasets. In the end, the ORL and Yale dataset are used for the experiments.
(2) This paper proposed a wavelet transform based recognition algorithm. The computing time of the traditional PCA-Based face recognition algorithm is very large. So the wavelet transform method is used to do the preprocessing. The method this paper proposed is different from the traditional wavelet transform method used in face recognition. In the proposed method, the detail subimage and the vertical direction subimage are combined as the PCA algorithm's training set and the probe image. The experiments results present that the speed of the training and recognition is six times faster than the traditional PCA algorithm introduced in the precious chapter while the correct recognition rate is almost equal to the traditional wavelet transform based face recognition method.
(3) PCA algorithm can't effectively use the training samples to improve the recognition rate while each class has much training samples. This paper proposed a method called PCA&SVM based on each class. After present PCA on each class, their eigenspace are got to train the corresponding Support Vector Machines respectively. Then the probe images are tested by the SVM. Because SVM has the strong ability of segmenting high dimension data and PCA can distill the eigenspace effectively, the result of the experiment is satisfied.
引文
1 Samal A and Iyengar P A. Automatic recognition and analysis of human faces and facial expressions: a survey. Pattern Recognition, 1992,25(1): 65-77.
2 Chellappa R, Wilson C L, Sirohey S. Human and machine recognition of faces: a survey. Proc. IEEE, 1995, 83(5): 705-740.
3 Rosenfeld A. Survey: Image analysis and computer vision: 1994. Computer Vision and Image Understanding, 1995,62(1): 90-143.
4 Rosenfeld A. Survey: Image analysis and computer vision: 1996. Computer Vision and Image Understanding, 1997,66(1): 33-93.
5 Baron R. Mechanisms of human facial recognition. Int. J. Man-Machine Studies, 1989,2,283-310.
6 Bruce V. Recognizing faces. London: Erlbaum, 1988.
7 Bichsel M. Perceiving and recognizing faces, Mind and Language, 1990, 342-364.
8 Ellis H et al. Aspects of face processing, Dordrecht: Nijhoff, 1986.
9 金忠．人脸图像特征抽取与维数研究．[博士学位论文]．南京：南京理工大学，1999．
10 Brunelli R and Poggio T. HyperBF networks for gender classification. Proc. DRRPA, Image Understanding Workshop, 1992, 311-314.
11 Sir Galton F. Numeralized profiles for classification and recognition. Nature 83,127-130(31 March 1910).
12 Harmon L D et al. Machine identification of human faces. Pattern Recognition, 1981, 13(2): 97-110.
13 Allen A L. Personal Descriptions. London,Butterworth,1950.
14 Parker F I,Computer Generated Animation of Faces. In Proceedings ACM ann Conference, 1972,1:451-457.
15 Parker F I,Computer Generated Animation of Faces. In Proceedings ACM ann Conference, 1972,1:451-457.
16 Kaya Y, Kobayashi K, A Basic study on Human Recognition. In Frontiers of Pattern Recognition. New York: Academic, 1971,265-289.
17 Kanad T, Picture processing system by computer and recognition of human face [Ph D Dissertation].Kyoto: Kyoto University, 1973.
18 Turk M and Pentland A. Eigenfaces for recognition. J. Cognitive Neuroscience, 1991, 3(1):71-86.
19 Juell P, Marsh R. A hierarchical neural network for human face detection. Pattern Recognition, 1996, 29(5):781-787.
20 Schofield A J et al. A system for counting people in video images using neural networks to identify the background scene. Pattem Recognition, 1996, 29(8):1425-1428.
21 Intrator N et al. Face recognition using a hybrid supervised/unsupervised neural network. Pattern Recognition Letters, 1996, 17(1):67-76.
22 Yoon K S et al. Hybrid approaches to frontal view face recognition using the hidden Markov model and neural network. Pattern Recognition, 1998,31(3):283-293
23 Roudey H A. Neural network-based face detection. Proc. of Image Understanding Workshop, 1996:725-735.
24 Ranganath S and Arun K. Face recognition using transform features and neural networks. Pattern Recognition, 1997,30(10): 1615-1622.
25 K.Sung and T.Poggio. CVPR'95:398-406.
26 K.Sung,T.Poggio. IEEE Trans. PAMI,1998,20:39-51.
27 H.A.Rowley et al. IEEE Trans. PAMI,1998,20:23-38.
28 S.Lin,S.Y.Kung,et al. IEEE Trans. NN,1997,8:114-132.
29 B.Moghaddam,A.Pentland. IEEE Trans. PAMI,1997,19:696-710.
30 M.A.Turk,A.P.Pentland. CVPR'91:586-591.
31 R.Brunelli,T.Poggio. Pattern Recognition, 1997,30:751-768.
32 G.Z.Yang et al. Pattern Recognition,1994,27:53-63.
33 C.C.Lin,W.C.Lin. Pattern Recognition,1996,19:129-146.
34 S.H.Jeng et al. Pattern Recognition,1998,3:273-282.
35 K.C.Yow et al. Image and Vision Computing,1997,15:713-735.
36 V.Govingdaraju. Int. J. Computer Vision,1996,19:129-146.
37 A.Tankus et al. PR Letters,1997,18:913-922.
38 C.H.Lee et al. Pattern Recognition,1996,29:1877-1899.
39 Y.Dai and Y.Nakano. Pattern Recognition,1996,29:1007-1017.
40 E.Saber et al. Pattern Recognition Letters,1998,19:669-680.
41 A.Samal,P.A.Iyengar. Pattern Recognition, 1992,25:65-77.
42 R.Chellappa et al. Procedings of IEEE,1995,83 :705-740.
43 H.Zabrodsky et al. IEEE Trans. PAMI,1995,17:1154-1166.
44 D.Reisfeld et al. Int. J. Computer Vision,1995,14:119-130.
45 Y.Adini et al. IEEE Trans. PAMl,1997,19:721-732.
46 X.Iia, MS. IEEE Trans PAMI,1995,17:1167-1176.
47 R.Brunelli,T.Piggio. IEEE Trans. PAMI,1993,15:1042-1052.
48 I.J.Cox,J.Ghosn,P.N.Yianilos. CVPR's96:209-216.
49 N.Roder,X.Li. Pattern Recognition,1996,29:209-216.
50 A.L.Yuille.J. Cognitive Neuroscience,1989,3:59-70.
51 K.M.Lam,H.Yan. Pattern Recognition,1995,29:771-779.
52 J.Ydeng,F.Lai. Pattern Recognition,1997,30:403-419.
53 H.Peng,D. Electronics Letters,1997,33:283-284.
54 K.L.Swets and J.Weng. IEEE Trans. PAMI,1996,18:831-836.
55 P.N.Belhumeur et al. IEEE Trans. PAMI,1997,19:711-720.
56 D.Velentin et al. Pattern Recognition,1994,27:1209-1230.
57 P.S.Penev,J.J.Atick. Network Compution&Neural Network,1996,7:477-490.
58 M.Lades et al. IEEE Trans. Computer,1993,42:300-311.
59 J.Zhang et al. Proc. IEEE,1997,85:1423-1435.
60 L.Wiskott. Pattern Recognition,1997,30:837-846.
61 L.Wiskott et al. IEEE Trans. PAMI,1997,19:775-779.
62 C.Nastar et al. Computer Vision and Image Understanding,1997,65:179-191.
63 B.Moghaddam et al. CVPR,1996
64 A.Lanitis et al. Image & Vision Computing,1995,13:393-401.
65 A.Lanitis et al. IEEE Trans. PAMI,1997,19:743-756.
66 N.Intrator, D.Reisfeld,Y.Yeshurun. PR Letters,1996,17:67-76.
67 S.Y.Lee et al. Pattern Recognition,1996,29:1863-1876.
68 S.Lawrence et al. IEEE Trans. NN,1997,8:98-113.
69 Y.Dai,Y.Nakano. Pattern Recognition, 1998,31:539-553.
70 S.Gutta,H.Wechsler. Pattern Recognition,1997,30:539-553.
71 P.J.Philips. IEEE Trans. Image Processing,1998,7:1150-1164.
72 C.Y.Lu et al. ICNNB,1998,645-648.
73 F.Goudail et al. IEEE Trans. PAMI,1996,18:1024-1028.
74 J.Benarie,D.Nandy. IEEE Trans. PAMI,1998,20:449-457.
75 K.M.Lam,H.Yan. IEEE Trans. PAMl,1998,20:673-686.
76 T.Vetter. Int. J. Computer Vision,1998,28:103-116.
77 A.R. Mirhosseini. Computer Vision and Image Understanding,1998,71:213-230.
78 Wendy.S.Yambor, Analysis of PCA-Based and Fisher Diseriminant-Based Image Recognition Algorithms, Computer Science Technical Report, Colorado State University 2000.
79 Yambor W., Draper B., and Beveridge J.R., Analysis of PCA-based Face Recognition Algorithms: Eigenvector Selection and Distance Measures. Second Workshop on Empirical Evaluation Methods in Computer Vision, 2000
80 杨福生．小波变换的工程分析与应用．北京：科学出版社，1999．
81 夏良正等．数字图像处理(修订版)．南京：东南大学出版社，1998．
82 Vapnik V., Lerner A. Pattern Recognition using Generalized Portrait Automation and Remote Control, 1963, 24: 6.
83 Kimeidorf G., Wahba G. Some Results on Tchebycheffian Spline Functions J. Math. Anal. Applic., 1971, 33(1):82—95.
84 Wahba G. Spline Models for Observational Data SIAM, CBMS-NSF Regional Conference Series, V59 1990.
85 Boser B, Guyon I, Vapnik V. A training algorithm for optimal margin classifiers, Fifth Annual Workshop on Computational Learning Theory. Pittsburgh: ACM Press, 1992.
86 Osuna E, Freund R, Girosi F. An Inproved Training Algorithm for Support Vector Machines. In: Principe J, Gile L, Morgan N, Wilson E eds., Proceedings of the 1997 IEEE Workshop on Neural Networks for Signal Processing, New York: IEEE, 1997, 276～285.
87 Joachims T. Making Large-Scale SVM Learning Practical In: Scholkopf B, Burges C J C, Smola A eds., Advances in Kernel Methods — Support Vector Learntng, Cambridge, MA: MIT Press, 1998, 169～184.
88 Platt J C. Fast Training of SVM Using Sequential Minimal Optimization. In: Scholkopf B, Burges C J C, Smola A J eds., Advances in Kernel Methods — Support Vector Learning, Cambridge, MA: MIT Press, 1998, 185～208.
89 Cristianini N, et al. Dynamically Adapting Kernels in Support Vector Machines. Neuro COLT: [Technical Report TR-1998-017]. Royal Holloway College.
90 萧嵘，孙晨，王继成等。一种具有容噪性能的SVM多值分类器。计算机研究与发展，2000，37(9)：1071-1075．
91 Vapnik V. The Nature of Statistical Learning Theory New York: Springer-Verlag, 1995.
92 周杰，卢春雨，张长水等。人脸自动识别方法综述。电子学报，2000，4．
2 Chellappa R, Wilson C L, Sirohey S. Human and machine recognition of faces: a survey. Proc. IEEE, 1995, 83(5): 705-740.
3 Rosenfeld A. Survey: Image analysis and computer vision: 1994. Computer Vision and Image Understanding, 1995,62(1): 90-143.
4 Rosenfeld A. Survey: Image analysis and computer vision: 1996. Computer Vision and Image Understanding, 1997,66(1): 33-93.
5 Baron R. Mechanisms of human facial recognition. Int. J. Man-Machine Studies, 1989,2,283-310.
6 Bruce V. Recognizing faces. London: Erlbaum, 1988.
7 Bichsel M. Perceiving and recognizing faces, Mind and Language, 1990, 342-364.
8 Ellis H et al. Aspects of face processing, Dordrecht: Nijhoff, 1986.
9 金忠．人脸图像特征抽取与维数研究．[博士学位论文]．南京：南京理工大学，1999．
10 Brunelli R and Poggio T. HyperBF networks for gender classification. Proc. DRRPA, Image Understanding Workshop, 1992, 311-314.
11 Sir Galton F. Numeralized profiles for classification and recognition. Nature 83,127-130(31 March 1910).
12 Harmon L D et al. Machine identification of human faces. Pattern Recognition, 1981, 13(2): 97-110.
13 Allen A L. Personal Descriptions. London,Butterworth,1950.
14 Parker F I,Computer Generated Animation of Faces. In Proceedings ACM ann Conference, 1972,1:451-457.
15 Parker F I,Computer Generated Animation of Faces. In Proceedings ACM ann Conference, 1972,1:451-457.
16 Kaya Y, Kobayashi K, A Basic study on Human Recognition. In Frontiers of Pattern Recognition. New York: Academic, 1971,265-289.
17 Kanad T, Picture processing system by computer and recognition of human face [Ph D Dissertation].Kyoto: Kyoto University, 1973.
18 Turk M and Pentland A. Eigenfaces for recognition. J. Cognitive Neuroscience, 1991, 3(1):71-86.
19 Juell P, Marsh R. A hierarchical neural network for human face detection. Pattern Recognition, 1996, 29(5):781-787.
20 Schofield A J et al. A system for counting people in video images using neural networks to identify the background scene. Pattem Recognition, 1996, 29(8):1425-1428.
21 Intrator N et al. Face recognition using a hybrid supervised/unsupervised neural network. Pattern Recognition Letters, 1996, 17(1):67-76.
22 Yoon K S et al. Hybrid approaches to frontal view face recognition using the hidden Markov model and neural network. Pattern Recognition, 1998,31(3):283-293
23 Roudey H A. Neural network-based face detection. Proc. of Image Understanding Workshop, 1996:725-735.
24 Ranganath S and Arun K. Face recognition using transform features and neural networks. Pattern Recognition, 1997,30(10): 1615-1622.
25 K.Sung and T.Poggio. CVPR'95:398-406.
26 K.Sung,T.Poggio. IEEE Trans. PAMI,1998,20:39-51.
27 H.A.Rowley et al. IEEE Trans. PAMI,1998,20:23-38.
28 S.Lin,S.Y.Kung,et al. IEEE Trans. NN,1997,8:114-132.
29 B.Moghaddam,A.Pentland. IEEE Trans. PAMI,1997,19:696-710.
30 M.A.Turk,A.P.Pentland. CVPR'91:586-591.
31 R.Brunelli,T.Poggio. Pattern Recognition, 1997,30:751-768.
32 G.Z.Yang et al. Pattern Recognition,1994,27:53-63.
33 C.C.Lin,W.C.Lin. Pattern Recognition,1996,19:129-146.
34 S.H.Jeng et al. Pattern Recognition,1998,3:273-282.
35 K.C.Yow et al. Image and Vision Computing,1997,15:713-735.
36 V.Govingdaraju. Int. J. Computer Vision,1996,19:129-146.
37 A.Tankus et al. PR Letters,1997,18:913-922.
38 C.H.Lee et al. Pattern Recognition,1996,29:1877-1899.
39 Y.Dai and Y.Nakano. Pattern Recognition,1996,29:1007-1017.
40 E.Saber et al. Pattern Recognition Letters,1998,19:669-680.
41 A.Samal,P.A.Iyengar. Pattern Recognition, 1992,25:65-77.
42 R.Chellappa et al. Procedings of IEEE,1995,83 :705-740.
43 H.Zabrodsky et al. IEEE Trans. PAMI,1995,17:1154-1166.
44 D.Reisfeld et al. Int. J. Computer Vision,1995,14:119-130.
45 Y.Adini et al. IEEE Trans. PAMl,1997,19:721-732.
46 X.Iia, MS. IEEE Trans PAMI,1995,17:1167-1176.
47 R.Brunelli,T.Piggio. IEEE Trans. PAMI,1993,15:1042-1052.
48 I.J.Cox,J.Ghosn,P.N.Yianilos. CVPR's96:209-216.
49 N.Roder,X.Li. Pattern Recognition,1996,29:209-216.
50 A.L.Yuille.J. Cognitive Neuroscience,1989,3:59-70.
51 K.M.Lam,H.Yan. Pattern Recognition,1995,29:771-779.
52 J.Ydeng,F.Lai. Pattern Recognition,1997,30:403-419.
53 H.Peng,D. Electronics Letters,1997,33:283-284.
54 K.L.Swets and J.Weng. IEEE Trans. PAMI,1996,18:831-836.
55 P.N.Belhumeur et al. IEEE Trans. PAMI,1997,19:711-720.
56 D.Velentin et al. Pattern Recognition,1994,27:1209-1230.
57 P.S.Penev,J.J.Atick. Network Compution&Neural Network,1996,7:477-490.
58 M.Lades et al. IEEE Trans. Computer,1993,42:300-311.
59 J.Zhang et al. Proc. IEEE,1997,85:1423-1435.
60 L.Wiskott. Pattern Recognition,1997,30:837-846.
61 L.Wiskott et al. IEEE Trans. PAMI,1997,19:775-779.
62 C.Nastar et al. Computer Vision and Image Understanding,1997,65:179-191.
63 B.Moghaddam et al. CVPR,1996
64 A.Lanitis et al. Image & Vision Computing,1995,13:393-401.
65 A.Lanitis et al. IEEE Trans. PAMI,1997,19:743-756.
66 N.Intrator, D.Reisfeld,Y.Yeshurun. PR Letters,1996,17:67-76.
67 S.Y.Lee et al. Pattern Recognition,1996,29:1863-1876.
68 S.Lawrence et al. IEEE Trans. NN,1997,8:98-113.
69 Y.Dai,Y.Nakano. Pattern Recognition, 1998,31:539-553.
70 S.Gutta,H.Wechsler. Pattern Recognition,1997,30:539-553.
71 P.J.Philips. IEEE Trans. Image Processing,1998,7:1150-1164.
72 C.Y.Lu et al. ICNNB,1998,645-648.
73 F.Goudail et al. IEEE Trans. PAMI,1996,18:1024-1028.
74 J.Benarie,D.Nandy. IEEE Trans. PAMI,1998,20:449-457.
75 K.M.Lam,H.Yan. IEEE Trans. PAMl,1998,20:673-686.
76 T.Vetter. Int. J. Computer Vision,1998,28:103-116.
77 A.R. Mirhosseini. Computer Vision and Image Understanding,1998,71:213-230.
78 Wendy.S.Yambor, Analysis of PCA-Based and Fisher Diseriminant-Based Image Recognition Algorithms, Computer Science Technical Report, Colorado State University 2000.
79 Yambor W., Draper B., and Beveridge J.R., Analysis of PCA-based Face Recognition Algorithms: Eigenvector Selection and Distance Measures. Second Workshop on Empirical Evaluation Methods in Computer Vision, 2000
80 杨福生．小波变换的工程分析与应用．北京：科学出版社，1999．
81 夏良正等．数字图像处理(修订版)．南京：东南大学出版社，1998．
82 Vapnik V., Lerner A. Pattern Recognition using Generalized Portrait Automation and Remote Control, 1963, 24: 6.
83 Kimeidorf G., Wahba G. Some Results on Tchebycheffian Spline Functions J. Math. Anal. Applic., 1971, 33(1):82—95.
84 Wahba G. Spline Models for Observational Data SIAM, CBMS-NSF Regional Conference Series, V59 1990.
85 Boser B, Guyon I, Vapnik V. A training algorithm for optimal margin classifiers, Fifth Annual Workshop on Computational Learning Theory. Pittsburgh: ACM Press, 1992.
86 Osuna E, Freund R, Girosi F. An Inproved Training Algorithm for Support Vector Machines. In: Principe J, Gile L, Morgan N, Wilson E eds., Proceedings of the 1997 IEEE Workshop on Neural Networks for Signal Processing, New York: IEEE, 1997, 276～285.
87 Joachims T. Making Large-Scale SVM Learning Practical In: Scholkopf B, Burges C J C, Smola A eds., Advances in Kernel Methods — Support Vector Learntng, Cambridge, MA: MIT Press, 1998, 169～184.
88 Platt J C. Fast Training of SVM Using Sequential Minimal Optimization. In: Scholkopf B, Burges C J C, Smola A J eds., Advances in Kernel Methods — Support Vector Learning, Cambridge, MA: MIT Press, 1998, 185～208.
89 Cristianini N, et al. Dynamically Adapting Kernels in Support Vector Machines. Neuro COLT: [Technical Report TR-1998-017]. Royal Holloway College.
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