相关投影分析在特征抽取中的应用研究
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摘要
特征抽取是模式识别领域最基本的问题之一。通过特征抽取,以较少的维数表示数据,用更为稳定的表达方式提高分类性能。近几十年来,在主成分分析、线性鉴别分析等线性鉴别特征抽取方法的基础上,典型相关分析(Canonical Correlation Analysis, CCA)、偏最小二乘(Partial Least Squares, PLS)等相关投影分析方法在数据处理与分析、回归分析与预测、鉴别信息抽取与融合等各个领域得到了广泛应用。特别是伴随着对相关投影分析的本质认识的不断深入,CCA、PLS与主成分分析(Principal Component Analysis, PCA)、线性鉴别分析(Linear Discriminant Analysis,LDA)之间的关系已被发现,前人的研究将利用相关投影分析抽取鉴别信息、进行信息融合的理论推到了一个新的阶段,具体的应用则更扩展到了模式分类与识别、图像重构与压缩、信息检索、回归分析等各个领域。正是因为相关投影分析在各个领域的成功应用,使其成为模式识别研究中最有活力、最有应用前景的领域之一。另一方面,相关投影分析从基础理论到具体应用,都有一些重要问题尚未解决,这激励着人们争相参与到此项研究中去。
CCA是实现信息融合的有力工具。随着用CCA抽取典型成分作为鉴别特征及用于多特征融合进行模式识别的成功应用,该方法又被推广到图像鉴别特征抽取中,并建立了CCA抽取鉴别特征的理论框架。
PLS回归分析提供了单因变量或多因变量对多自变量的回归建模方法,在回归建模的同时,不仅实现了原始数据的压缩,也消除了对系统无解释意义的干扰信息(噪声)。由于PLS解决了以往用普通多元回归分析方法无法解决的难题,因此该方法的理论研究进展非常迅速,应用领域已扩展到机械、生物、地质、医学、社会学以及经济学等领域。PLS模型的鲁棒性使其成为回归分析、维数压缩和分类技术的有力工具之一。
本文工作主要包括如下内容：
(1)进一步完善了基于CCA和PLS的相关投影分析,并且用于单特征、组合特征抽取和图像分类与识别的理论框架。讨论了CCA抽取鉴别特征的原则和特征组合,以及在正交约束和统计不相关约束条件下CCA和PLS抽取特征的性能,并与传统方法如PCA、LDA进行了对比。实验结果表明,相关投影分析能够更有效地抽取鉴别特征,特别是对称性的双特征,如人的左右眼、左右手掌的鉴别特征抽取有着更好的表现。
(2)在介绍基于图像矩阵的二维相关投影分析的基础上,引入二维典型相关分析(Two-dimensional Canonical Correlation Analysis,2DCCA)和二维偏最小二乘(Two-dimensional Partial Least Squares,2DPLS)的基本理论,深入讨论了2DCCA与(Two-dimensional Linear Discriminant Analysis,2DLDA)的关系,证明了在两类类标编码情况下,二者仍存在等价关系。
(3)分析了基于类标号的相关投影分析的缺陷,在此基础上提出了基于样本标号的相关投影分析,并将其推广到二维情况。基于同样原因,提出了模糊相关投影分析。实验结果表明,两种改进算法都可以有效地提高鉴别特征抽取性能。在ORL、AR等人脸图像数据库、中科院自动化所掌纹图像库(CASIA-Palmprint)、香港理工大学掌纹图像库(PolyU Palmprint)的实验基础上,在构建的战斗机卫星图像数据集上进一步验证了本文算法的有效性,也为统计模式识别在基于遥感图像的重要目标识别做了有益的尝试。
(4)基于回归分析理论,从分析与预测的实际出发,运用PLSR对美国大选建模,寻找候选人得票率与国民经济发展等因素的相关关系。从而成功地将PLSR应用到辅助分析中去,拓展了分析与预测的研究方法和手段。
Discriminant feature extraction is one of the basic problems of pattern recognition. Data can be described with fewer dimension information by feature extraction, which can improve recognition rate effectively with more steady data description. Recently, on the basis of linear discriminant feature extraction methods such as principal component analysis (PCA), linear discriminant analysis (LDA), correlation projection analysis methods such as canonical correlation analysis (CCA), partial least squares (PLS) have been used widely in many fields:data processing and analysis, regression analysis and prediction, discriminant feature extraction and fusion and so on. Especially, with the deepening understanding to the essence of correlation projection analysis, people have found the relations between CCA, PLS, PCA and LDA. Earlier study of correlation projection analysis has put the theory of discriminant feature extraction and information fusion to a new stage. The applications have also expanded to pattern classification and recognition, image compression and reconstruction, information retrieval, regression analysis, and so on. As the result of its successful application in many fields, correlation projection analysis has been one of the most lively and potential fields. On the other hand, there are many important problems from basic theory to application to be solved, which inspirit people to participate in the studies.
As we know, CCA is effective means for information fusion. By the successful application of discriminant feature extraction and multi-feature fusion with CCA, it has also expanded to image's discriminant feature extraction, and the theoretic frameworks have been established.
PLS regression analysis provides a regression modeling method for single/multi dependent variables with independent ones. On the course of regression modeling, original data are compressed, and interfering information (noise) is removed at the same time. PLS has solved the problems which cannot be solved with classical multivariate analysis methods, so the theoretic research of this method has developed rapidly. Its applying fields have extended to mechanics, biology, geology, medicine, sociology and economics. The robustness of PLS makes it become one of the most effective tools for regression analysis, dimension reduction and classifying technique.
Our work mainly includes the following parts:
(1) On the basis of other persons' work, we further perfect the theoretical framework of single/combined feature extraction and image classification & recognition with correlation projection analysis based on CCA&PLS. We discuss the principle of feature extraction and feature combine with CCA, and the capability of feature extraction with CCA&PLS under orthogonal constraints or statistical uncorrelative (conjugate orthogonal) constraints, then compare with classical methods such as PCA and LDA. The results of experiments show that correlation projection analysis is more efficient in discriminant feature extraction, especially in the case of symmetrical dual-features such as human being's dual-eyes, dual-palmprints, and we will get more ideal results.
(2)On the basis of two-dimensional correlation projection analysis based on image matrices, we introduce the basic theory of 2DCCA and 2DPLS, and discuss the relationship between 2DLDA and 2DCCA. We prove that they are equivalent in c and c-1 class label encoding cases for discriminant feature extraction.
(3)We analyze the defects of correlation projection analysis based on class label encoding, then introduce correlation projection analysis based on sample label encoding, and further expand it to two-dimensional cases. For the same reason, we introduce fuzzy correlation projection analysis and give new algorithms. The results of experiments show that both methods can improve the performance of feature extraction. On the basis of experiments on ORL and AR face databases, CASIA-Palmprint and PolyU Palmprint databases, combining with our practical work, we build a remote sense image database of fighters. Experiment results on it show that our algorithms are efficient and robust. Moreover it is an attempt for important targets recognition in remote sense images.
(4)On the basis of regression theories and for the purpose of analysis and prediction, we use PLSR to model US presidential election in order to explore the relationship between candidates' votes and domestic economic development and other factors. As a result, we can deal with analysis and prediction with PLS successfully, and achieve preferable results. We get the purpose of "quantitating qualitative problems, and qualitatively analyzing quantitative results", and enrich the means for analysis and prediction.
CCA是实现信息融合的有力工具。随着用CCA抽取典型成分作为鉴别特征及用于多特征融合进行模式识别的成功应用,该方法又被推广到图像鉴别特征抽取中,并建立了CCA抽取鉴别特征的理论框架。
PLS回归分析提供了单因变量或多因变量对多自变量的回归建模方法,在回归建模的同时,不仅实现了原始数据的压缩,也消除了对系统无解释意义的干扰信息(噪声)。由于PLS解决了以往用普通多元回归分析方法无法解决的难题,因此该方法的理论研究进展非常迅速,应用领域已扩展到机械、生物、地质、医学、社会学以及经济学等领域。PLS模型的鲁棒性使其成为回归分析、维数压缩和分类技术的有力工具之一。
本文工作主要包括如下内容：
(1)进一步完善了基于CCA和PLS的相关投影分析,并且用于单特征、组合特征抽取和图像分类与识别的理论框架。讨论了CCA抽取鉴别特征的原则和特征组合,以及在正交约束和统计不相关约束条件下CCA和PLS抽取特征的性能,并与传统方法如PCA、LDA进行了对比。实验结果表明,相关投影分析能够更有效地抽取鉴别特征,特别是对称性的双特征,如人的左右眼、左右手掌的鉴别特征抽取有着更好的表现。
(2)在介绍基于图像矩阵的二维相关投影分析的基础上,引入二维典型相关分析(Two-dimensional Canonical Correlation Analysis,2DCCA)和二维偏最小二乘(Two-dimensional Partial Least Squares,2DPLS)的基本理论,深入讨论了2DCCA与(Two-dimensional Linear Discriminant Analysis,2DLDA)的关系,证明了在两类类标编码情况下,二者仍存在等价关系。
(3)分析了基于类标号的相关投影分析的缺陷,在此基础上提出了基于样本标号的相关投影分析,并将其推广到二维情况。基于同样原因,提出了模糊相关投影分析。实验结果表明,两种改进算法都可以有效地提高鉴别特征抽取性能。在ORL、AR等人脸图像数据库、中科院自动化所掌纹图像库(CASIA-Palmprint)、香港理工大学掌纹图像库(PolyU Palmprint)的实验基础上,在构建的战斗机卫星图像数据集上进一步验证了本文算法的有效性,也为统计模式识别在基于遥感图像的重要目标识别做了有益的尝试。
(4)基于回归分析理论,从分析与预测的实际出发,运用PLSR对美国大选建模,寻找候选人得票率与国民经济发展等因素的相关关系。从而成功地将PLSR应用到辅助分析中去,拓展了分析与预测的研究方法和手段。
Discriminant feature extraction is one of the basic problems of pattern recognition. Data can be described with fewer dimension information by feature extraction, which can improve recognition rate effectively with more steady data description. Recently, on the basis of linear discriminant feature extraction methods such as principal component analysis (PCA), linear discriminant analysis (LDA), correlation projection analysis methods such as canonical correlation analysis (CCA), partial least squares (PLS) have been used widely in many fields:data processing and analysis, regression analysis and prediction, discriminant feature extraction and fusion and so on. Especially, with the deepening understanding to the essence of correlation projection analysis, people have found the relations between CCA, PLS, PCA and LDA. Earlier study of correlation projection analysis has put the theory of discriminant feature extraction and information fusion to a new stage. The applications have also expanded to pattern classification and recognition, image compression and reconstruction, information retrieval, regression analysis, and so on. As the result of its successful application in many fields, correlation projection analysis has been one of the most lively and potential fields. On the other hand, there are many important problems from basic theory to application to be solved, which inspirit people to participate in the studies.
As we know, CCA is effective means for information fusion. By the successful application of discriminant feature extraction and multi-feature fusion with CCA, it has also expanded to image's discriminant feature extraction, and the theoretic frameworks have been established.
PLS regression analysis provides a regression modeling method for single/multi dependent variables with independent ones. On the course of regression modeling, original data are compressed, and interfering information (noise) is removed at the same time. PLS has solved the problems which cannot be solved with classical multivariate analysis methods, so the theoretic research of this method has developed rapidly. Its applying fields have extended to mechanics, biology, geology, medicine, sociology and economics. The robustness of PLS makes it become one of the most effective tools for regression analysis, dimension reduction and classifying technique.
Our work mainly includes the following parts:
(1) On the basis of other persons' work, we further perfect the theoretical framework of single/combined feature extraction and image classification & recognition with correlation projection analysis based on CCA&PLS. We discuss the principle of feature extraction and feature combine with CCA, and the capability of feature extraction with CCA&PLS under orthogonal constraints or statistical uncorrelative (conjugate orthogonal) constraints, then compare with classical methods such as PCA and LDA. The results of experiments show that correlation projection analysis is more efficient in discriminant feature extraction, especially in the case of symmetrical dual-features such as human being's dual-eyes, dual-palmprints, and we will get more ideal results.
(2)On the basis of two-dimensional correlation projection analysis based on image matrices, we introduce the basic theory of 2DCCA and 2DPLS, and discuss the relationship between 2DLDA and 2DCCA. We prove that they are equivalent in c and c-1 class label encoding cases for discriminant feature extraction.
(3)We analyze the defects of correlation projection analysis based on class label encoding, then introduce correlation projection analysis based on sample label encoding, and further expand it to two-dimensional cases. For the same reason, we introduce fuzzy correlation projection analysis and give new algorithms. The results of experiments show that both methods can improve the performance of feature extraction. On the basis of experiments on ORL and AR face databases, CASIA-Palmprint and PolyU Palmprint databases, combining with our practical work, we build a remote sense image database of fighters. Experiment results on it show that our algorithms are efficient and robust. Moreover it is an attempt for important targets recognition in remote sense images.
(4)On the basis of regression theories and for the purpose of analysis and prediction, we use PLSR to model US presidential election in order to explore the relationship between candidates' votes and domestic economic development and other factors. As a result, we can deal with analysis and prediction with PLS successfully, and achieve preferable results. We get the purpose of "quantitating qualitative problems, and qualitatively analyzing quantitative results", and enrich the means for analysis and prediction.
引文
[1]Andrew R. Webb. Statistical Pattern Recognition, Second Edition. John Wiley & Sons, Inc,2002.
[2]边肇祺,张学工.模式识别(第二版).北京：清华大学出版社,2000.
[3]John Shawe-Taylor, Nello Cristianini. Kernel Methods for Pattern Analysis. Cambridge University Press,2004.
[4]张学工译.统计学习理论的本质(第二版).北京：清华大学出版社,2000.
[5]李国正,王猛,曾华军等译.支持向量机导论.北京：电子工业出版社,2004.
[6]Liu C J, Wechsler H. A shape-and texture-based enhanced Fisher classifier for face recognition. IEEE Trans. Image Processing,2001,10(4):598-608.
[7]Yang J, Yang J Y. Generalized K-L transform based combined feature extraction. Pattern Recognition,2002,35(1):295-297.
[8]Yang J, Yang J Y, Zhang D, Lu J F. Yang J Y. Feature fusion:parallel strategy vs. serial strategy. Pattern Recognition,2003,36 (6):1369-1381.
[9]杨健.线性投影分析的理论与算法及其在特征抽取中的应用.南京：南京理工大学博士论文,2002.
[10]Yang J, Yang J Y, Frangi A F, Zhang D. Uncorrelated Projection Discriminant Analysis and Its Application to Face Image Feature Extraction. International Journal of Pattern Recognition and Artificial Intelligence,2003,17(8):1325-1347.
[11]Yang J, Zhang D, Xu Y, Yang J Y. Two-dimensional discriminant transform for face recognition. Pattern Recognition,2005,38(7):1125-1129.
[12]M. Borga, T. Landelius, H. Knutsson. A unified approach to PCA, PLS, MLR and CCA, Technical Report, LiTH-ISY-R-1992, Linkoping University, Sweden,1992.
[13]陆璇等译.实用多元统计分析(第四版).北京：清华大学出版社,2003.
[14]袁志发,周静芋.多元统计分析.北京：科学出版社,2002.
[15]James Lattin, J. Douglas Carroll, Paul E. Green. Analyzing Multivariate Data北京：机械工业出版社,2004.
[16]David G. Kleinbaum, Lawrence L.Kupper, Keith E. Muller, Azhar Nizam. Applied Regression Analysis and Other Multivariable Methods (Third Edition)北京：机械工业出版社,2006.
[17]孙权森.基于相关投影分析的特征抽取与图像识别研究.南京：南京理工大学博士论文,2006.
[18]孙挺凯.增强型典型相关分析研究与应用.南京：南京航空航天大学博士论文,2006.
[19]Long Han. kernel Partial Least Squares(K-PLS) for Scientific Data Mining. New York: Rensselaer Polytechnic Institute PHD thesis,2007.
[20]孙平,徐宗本,申建中.基于核化原理的非线性典型相关判别分析.计算机学报,2004,27(6)：789-795.
[21]Sun Q S, Zeng S G, Liu Y, Heng P A, Xia D S. A New Method of Feature Fusion and Its Application in Image Recognition. Pattern Recognition,2005,38(12):449-452.
[22]Sun Q S, Jin Z, Heng P A, Xia D S. A Novel Feature Fusion Method Based on Partial Least Squares Regression. The third International Conference on Advances in Pattern Recognition(Bath, UK, August 2005), Lecture Notes in Computer Science(LNCS), Springer-Verlag, Heidelberg, Berlin,2005,3686:268-277.
[23]Sun Q S, Liu Z D, Heng P A, Xia D S. A Theorem on the Generalized Canonical Projective Vectors. Pattern Recognition,2005,38(3):449-452.
[24]Sun Q S, Heng P A, Jin Z, Xia D S. Face Recognition Based on Generalized Canonical Correlation Analysis. International Conference on Intelligent Computing(Hefei, China, August 2005), Lecture Notes in Computer Science(LNCS), Springer-Verlag, Heidelberg, Berlin,2005,3645:958-967.
[25]孙权森,曾生根,王平安,夏德深.典型相关分析的理论及其在特征融合中的应用,计算机学报,2005,28(9)：1524-1533.
[26]孙权森,曾生根,杨茂龙,王平安,夏德深.基于典型相关分析的组合特征抽取及脸像鉴别,计算机研究与发展,2005,42(4)：614-621.
[27]M.Sargin, E. Erzin, Y. Yemez, et al. Multimodal speaker identification using canonical correlation analysis. IEEE International Conference on Acoustics, Speech and Signal Processing,2006(1):Ⅰ-613-Ⅰ-616.
[28]A. Pezeshki, A-Sadjadi, Scharf, et al. A canonical correlation-based feature extraction method for underwater target classification, Oceans'02 MTS/IEEE,2002 1:29-37.
[29]M. Hasan. A new approach for computing canonical correlations and coordinates. International Symposium on Circuits and Systems,2004,3:309-312.
[30]Nguyen D V, Rocke D M. Tumor classification by partial least squares using microarray gene expression data. Bioinformatics,2002,18(1):39-50.
[31]Nguyen D V, Rocke D M. Multi-class cancer classification via partial least squares with gene expression problems. Bioinformatics,2002,18(9):1216-1226.
[32]Nguyen D V, Rocke D M. Partial least squares proportional hazard regression for application to DNA microarraysurvival data. Bioinformatics,2002,18(12): 1625-1632.
[33]Miguel P E, Michel T. Prediction of clinical outcome with microarray data:a partial least squares discriminant analysis (PLS-DA) approach. Hum Genet,2003,112: 581-592.
[34]A. Nielsen. Multiset canonical correlations analysis and multispectral, truly multitemporal remote sensing data. IEEE Transactions on Image Processing,2002,11: 293-305.
[35]H. Ichihashi, K.Honda, S. Araki. Fuzzy canonical correlation and cluster analysis for brain mapping on long term memory consolidated by mnemonics. IEEE International Conference on Fuzzy Systems,2004,1(1):155-160.
[36]Y. Hel-Or, The canonical correlations of color images and their use for demosaicing, HP Labs Technical Report, HPL-2003-164(R.1), February 2004.
[37]Y. Yamanishi, J.-P. Vert, A. Nakayal, et al. Extraction of correlated gene clusters from multiple genomic data by generalized kernel canonical correlation analysis. Bioinformatics,2003,19(1), pp.i323-i330.
[38]M. Borga, H. Knutsson. A canonical correlation approach to blind source separation. Technical Report, LiU-IMT-EX-0062, Department of Biomedical Engineering, Linkoping University,2001.
[39]J. Galy, C. Adnet. Canonical correlation analysis:a blind source separation using non-circularity. Neural Networks for Signal Processing X, Proceedings of the 2000 IEEE Signal Processing Society Workshop,2000,1(11-13):465-473.
[40]M. Borga, O. Friman, P. Lundbergy, H. Knutsson. A canonical correlation approach to exploratory data analysis in fMRI. Proceedings of the ISMRM Annual Meeting, Honolulu, Hawaii,2002.
[41]J.K.Thomas, L.L.Scharf. Canonical correlations and canonical time series, IEEE International Conference on Acoustics, Speech, and Signal Processing,1996,3: 1637-1640.
[42]P. Schreier, L. Scharf, Canonical coordinates for transform coding of noisy sources, IEEE Transactions on signal processing,2006,54(1):235-243.
[43]M Kuss, T. Graepel. The geometry of kernel canonical correlation analysis. Max Planck Institute for Biological Cybernetics Technical Report No.108, May 2003.
[44]W. Zheng; X. Zhou; C. Zou et al. Facial expression recognition using kernel canonical correlation analysis (KCCA). IEEE Transactions on Neural Networks,2006,17(1): 233-238.
[45]A. Pezeshki, L. Scharf, Azimi-Sadjadi, et al. Empirical canonical correlation analysis in subspaces. Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers,2004,1:994-997.
[46]M. Loog, B. Ginneken, R.P.W. Duin. Dimensionality reduction of image features using the canonical contextual correlation projection. Pattern Recognition,2005,38(12): 2409-2418.
[47]P. Lai, S. Chuang, C Fyfe. Power load forecasting using neural canonical correlates. International Conference on Pattern Recognition,2000.
[48]T. Melzer, M. Reiter, H. Bischof, Appearance models based on kernel canonical correlation analysis, Pattern Recognition,2003,36(9):1961-1971.
[49]B. Fortuna. Kernel canonical correlation analysis with applications. In:SIKDD 2004 at Multiconference, Ljubljana, Slovenia.2004.
[50]D.R. Hardoon, S. Szedmak, J. Shawe-Taylor. Canonical correlation analysis:an overview with application to learning methods. Neural Computation 2004,16: 2639-2664.
[51]T. Gestel, J. Suykens, J. De Brabanter, et al. Kernel canonical correlation analysis and least squares support vector machines. In:Proc. of the International Conference on Artificial Neural Networks,2001,384-389.
[52]Y. He, L. Zhao, C. Zou. Face Recognition Based on PCA/KPCA plus CCA. In:L. Wang, K. Chen, and Y.S. Ong (Eds.):ICNC 2005, Berlin Heidelberg, Springer-Verlag, 2005, LNCS 3611, pp.71-74.
[53]S. Mika, G. Ratsch, J. Weston, B. Scholkopf, K-R. Muller. Fisher discriminant analysis with kernels. In:IEEE Neural Networks for Signal Processing Workshop,1999, 41-48.
[54]Matthew L. Barker. Partial least squares for discrimination. Lexington, Kentucky: University of Kentucky PHD thesis,2000.
[55]M. Yamada, A. Pezeshki, M. Azimi-Sadjadi. Relation between kernel CCA and kernel FDA. IEEE International Joint Conference on Neural Networks,2005,1(1):226-231.
[56]Colin Fyfe, Gayle Leen, Pei Ling Lai. Gaussian processes for canonical correlation analysis, Neurocomputing,2008 (71):3077-3088.
[57]Thomas Melzer. Generalized canonical correlation analysis for object recognition. [ph.D Dissertations], Vienna University of Technology,2002.
[58]M. Hasan. Information criteria for reduced rank canonical correlation analysis. IEEE International Joint Conference on Neural Networks,20043:2215-2220.
[59]P. Lai, C. Fyfe. Neural implementation of canonical correlation analysis. Neural Networks,1999,12(10):1391-1397.
[60]Y. Takane,Y. Oshima-Takane. Nonlinear generalized canonical correlation analysis by neural network models. In:Nishisato, S. et al. (Eds.), Measurement and Multivariate Analysis, Tokyo, Springer Verlag,2002, pp.183-190.
[61]X. Yin. Canonical correlation analysis based on information theory. Journal of Multivariate Analysis,2004,91(2):161-176.
[62]M. Barker, W. Rayens. Partial least squares for discrimination. Journal of Chemometrics,2003,17:166-173.
[63]Baek J, Kim M. Face recognition using partial least squares components. Pattern Recognition,2004,37(6):1303-1306.
[64]王惠文.偏最小二乘回归方法及其应用.北京：国防工业出版社,1999.
[65]王惠文,吴载斌,孟洁.偏最小二乘回归的线性与非线性方法.北京：国防工业出版社,2006.
[66]Vincenzo Esposito Vinzi, Michel Tenenhaus, Rong Guan. Proceedings of the 6th International Conference on Partial Least Squares and Related Methods. Beijing: Publishing House of Electronics Industry,2009.
[67]Du H Q, Ge H L et al. A new classifier for remote sensing data classification:partial least squares.2008 International Workshop on Earth Observation and Remote Sensing Applications.
[68]Kirby M, Sirovich L. Application of the K-L procedure for the characterization of human faces. IEEE Trans. Pattern Anal. Machine Intell.,1990,12(1):103-108.
[69]Turk M, Pentland A. Face processing:models for recognition. Proc. Intelligent Robots and Computer Vision Ⅷ, SPIE,1989,192:22-32.
[70]Turk M, Pentland A. Eigenfaces for recognition. J. Cognitive Neuroscience,1991,3(1): 71-86.
[71]Turk M, Pentland A. Face recognition using Eigenfaces. Proc. IEEE Conf. On Computer Vision and Pattern Recognition,1991,586-591.
[72]王建国.特征抽取方法研究及其在人脸识别中的应用.南京：南京理工大学博士论文,2008.
[73]Yang M H. Kernel Eigenfaces vs. Kernel Fisherfaces:Face Recognition Using Kernel Methods. Proceedings of the Fifth International Conference on Automatic Face and Gesture Recognition (FG), Washington D. C.,2002,215-220.
[74]金忠.人脸图像特征抽取与维数研究.南京：南京理工大学博士论文,1999.
[75]Jin Z, Yang J Y, Hu Z S, Lou Z. Face Recognition based on uncorrelated discriminant transformation. Pattern Recognition,2001,34(7):1405-1416.
[76]Jin Z, Yang J Y, Tang Z M, Hu Z S. A theorem on uncorrelated optimal discriminant vectors. Pattern Recognition,2001,34(10):2041-2047.
[77]Belhumeur P N, Hespanha J P, Kriegman D J. Eigenfaces vs. Fisherfaces:Recognition using class specific linear projection. IEEE Trans.Pattern Anal. Machine Intell.,1997, 19(7):711-720.
[78]Swets D L, Weng J. Using discriminant eigenfeatures for image retrieval. IEEE Trans. Pattern Anal. Machine Intell.,1996,18(8):831-836.
[79]杨健,杨静宇,叶晖.Fisher线性鉴别分析的理论及其应用.自动化学报,2003,29(4)：481-494.
[80]Hong Z Q, Yang J Y, et al. Optimal discriminant plane for a small number of samples and design method of classifier on the plane. Pattern Recognition,1991,24(4): 317-324.
[81]Liu K, Yang J Y, et al. An efficient algorithm for Foley-Sammon optimal set of discriminant vectors by algebraic method. International Journal of Pattern Recognition and Artificial Intelligence,1992,6(5):817-829.
[82]Guo G, et al. Face recognition by support vector machines. Proc.4th IEEE intern. Conf. Automatic Face and Gesture Recognition,2000,196-201.
[83]Guo Y F, Shu T T, Yang J Y. Feature extraction method based on the generalized Fisher Discriminant criterion and face recognition. Pattern Analysis & Application,2001, 4(1):61-66.
[84]Chen L F, Liao H M, Lin J C, Ko M T, Yu G J. A new LDA-based face recognition system which can solve the small sample size problem. Pattern Recognition,2000, 33(10):1713-1726.
[85]Hua Yu, Jian Yang, A direct LDA algorithm for high-dimensional data—with application to face recognition, Pattern Recognition.2001,34(11):2067-2070.
[86]杨健,杨静宇,金忠.最优鉴别特征的抽取及图像识别,计算机研究与发展,2001,38(11),pp.1331-1336.
[87]Kong H, Wang L, Teoh E K, Wang J G, Venkateswarlu R. A framework of 2D Fisher discriminant analysis:application to face recognition with small number of training samples. IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR),2005,2:1083-1088.
[88]严云洋.图像的特征抽取方法及其应用研究.南京：南京理工大学博士论文,2008.
[89]郭志波.人脸快速检测和特征抽取方法的研究.南京：南京理工大学博士论文,2007.
[90]Bartlett M.S., Movellan J.R., Sejnowski T.J. Face Recognition by Independent Component Analysis. IEEE Trans Neural Networks,2002.13(6):1450-1464.
[91]Liu C.J., Wechsler H. Independent component analysis of Gabor features for face recognition.2003,14(4):919-928.
[92]郭志波,杨静宇,刘华军.基于矩阵完备投影的快速主分量分析算法,中国图像图形学报,2007.12(4)：628-632.
[93]Hotelling H. Relations between two sets of variates. Biometrika,1936,8:321-377.
[94]Borga M. Learning Multidimensional Signal Processing. Linkoping Studies in Science and Technology, Dissertations, vol.531, Department of Electrical Engineering, Linkoping University, Linkoping, Sweden,1998.
[95]Tingkai Sun, Songcan Chen. Locality preserving CCA with applications to data visualization and pose estimation. Image and Vision Computing,2007,25(5):531-543.
[96]Grenier Y. Speaker adaptation through canonical correlation analysis. In:Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP,1980,5: 888-891.
[97]Choukri K, Chollet G, Grenier Y. Spectral transformations through canonical correlation analysis for speaker adptation in ASR. In:Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP,1986,2659-2662.
[98]Choi H C, King R W. Speaker adaptation through spectral transformation for HMM based speech recognition. IEEE International Symposium on Speech, Image Processing and Neural Networks,1994,2:686-689.
[99]Weenink D. Canonical Correlation Analysis. Institute of Phonetic Sciences, University of Amsterdam, Proceedings,2003,25:81-99.
[100]Bartlett M S. Further aspects of the theory of multiple regression. Proceedings of the Cambridge Philosophical Society,1938,34:33-40.
[101]L. Hoegaerts, J.A.K. Suykens, J. Vandewalle, B. De Moor. Subset based least squares subspace regression in RKHS. Elsevier Science,2004.
[102]Tingkai Sun, Songcan Chen. Class label versus sample label-based CCA. Applied Mathematics and Computation,2007,185(1):272-283.
[103]Yanyan Liu, Xiuping Liu, Zhixun Su. A new fuzzy approach for handling class labels in canonical correlation analysis. Neurocomputing,2008(71),1735-1740.
[104]Fu-Chang Liu, Jian Zhang, Quan-Sen Sun, De-Shen Xia. Generalized Canonical Correlation Analysis Using GSVD.2008 International Symposium on Computer Science and Computational Technology.200,136-141.
[105]Wold S, Martens H, Wold H. The Multivariate Calibration Problem in Chemistry Solved by the PLS Method. Proceedings of Conference on Matrix Pencils, Lecture Notes in Mathematics, Springer, Heidelberg,1983,286-293.
[106]Parthasarathy K, Jay H L, Victor S, Gopal A K. Partial least squares (PLS) based monitoring and control of batch digesters. Journal of Process Control,2000,10: 229-236.
[107]Yang Maolong, Mao Weihao, Sun Quansen, Xia Deshen. Sample labled-based PLS and feature extraction. Proceedings of the 6th International Conference on Partial Least Squares and Related Methods. Beijing:Publishing House of Electronics Industry. 2009,127-131.
[108]Jeronimo Arenas-Garcia, Gustavo Camps-Valls. Feature extraction from remote sensing data using kernel orthonormalized PLS.2007.
[109]Mattias Rantalainen, Max Bylesjo, etc. Kernel-based orthogonal projections to latent structures (K-OPLS). JOURNAL OF CHEMOMETRICS.2007; 21:376-385.
[110]孙宁等.基于2维偏最小二乘法的图像局部特征提取及其在面部表情识别中的应用.中国图像图形学报.2007,12(5),847-853.
[111]孙权森,陈强,夏德深.基于偏最小二乘分析的人脸表示与识别.江南大学学报.2008,7(1),1-5.
[112]Svante Wold, Johan Trygg, Anders Berglund, Henrik Antti. Some recent developments in PLS modeling. Chemometrics and Intelligent Laboratory Systems. 2001,58,131-150.
[113]Svante Wold, Michael Sjostrom, Lennart Eriksson. PLS-regression:a basic tool of chemometrics.Chemometrics and Intelligent Laboratory Systems.2001,58,109-130.
[114]Svante Wold. Personal memories of the early PLS development. Chemometrics and Intelligent Laboratory Systems.2001(58):83-84.
[115]Yushu Liu, William Rayens. PLS and dimension reduction for classification.Computational Statistics.2007(22),189-208.
[116]Max Bylesjo, Mattias Rantalainen, Olivier Cloarec, Jeremy K. Nicholson, Elaine Holmesand Johan Trygg. OPLS discriminant analysis:combining the strengths of PLS-DA and SIMCA classification. Journal of Chemometrics 2006(20):341-351.
[117]A.Hoskuldsson PLS Regression Methods. Journal of Chemometrics,1988,2: 211-228.
[118]A.Hoskuldsson Causal and path modeling. Chemometrics and Intelligent Laboratory Systems,2001,58:287-311.
[119]Liu K, Cheng Y Q, Yang J Y. Algebraic feature extraction for image recognition based on an optimal discriminant criterion. Pattern Recognition,1993,26 (6): 903-911.
[120]Yang Jian, Zhang David, Yang Jingyu. Two-dimensional PCA:a new approach to appearance-based face representation and recoginition. Pattern Analysis and Machine Intelligence.2004,26 (1):131-137.
[121]Wang Liwei, Wang Xiao, Zhang Xuerong, et al. The equivalence of two dimensional PCA and line-based PCA. Pattern Recognition Letters.2005,26(1):57-60.
[122]徐勇,杨健,赵英男,宋枫溪,杨静宇.一种缩减图像维数的方法及其在人脸图像上的应用.电子与信息学报.2008,30(1)：180-184.
[123]张生亮,谢永华,杨静宇.一种双向压缩的二维特征抽取算法及其应用.计算机应用研究.2006,23(5)：63-69.
[124]Sun Ho Lee, Seungjin Choi. Two-dimensional canonical correlation analysis. IEEE Signal Processing Letters.2007,14(10):1-4.
[125]Cai-rong Zou, Ning Sun, Zhen-hai Ji, Li Zhao.2DCCA:a novel method for small sample size face recognition. IEEE Workshop on Applications of Computer Vision(WACV07).2007,149-154.
[126]周晓彦,郑文明,赵力,邹采荣.基于偏最小二乘回归的人脸身份和表情同步识别方法.中国图象图形学报.2009,14(5)：801-808.
[127]Mao-long Yang, Quan-sen Sun, De-shen Xia. Two-dimensional partial squares and its application in image recognition. Proceedings of the 4th International Conference on Intelligence Computing (ICIC'08).2008,208-215.
[128]Yang Maolong, Mao Weihao, Sun Quansen, Xia Deshen. Combine Feature Extraction of Palmprint and Face Images Based on PLS. Proceedings of the 6th International Conference on Partial Least Squares and Related Methods. Beijing: Publishing House of Electronics Industry.2009,324-131.
[129]Ben Niu, Qiang Yang, et al. Two-dimensional laplacianfaces method for face recognition. Pattern Recognition.2007.
[130]Dewen Hu, Guiyu Feng, Zongtan Zhou. Two-dimensional locality preserving projections (2DLPP) with its application to palmprint recognition. Pattern Recognition. 2007,40:339-342.
[131]Sibao Chen, Haifeng Zhao, Min Kong, Bin Luo.2D-LPP:A two-dimensional extension of locality preserving projections. Neurocomputing.2007,70:912-921.
[132]Xin Pan, Qiu-Qi Ruan. Palmprint recognition with improved two-dimensional locality preserving projections. Image and Vision Computing.2008.
[133]张润楚.多元统计分析.北京：科学出版社,2007.
[134]金钟,杨静宇,陆建峰.一种具有统计不相关性的最佳鉴别矢量集.计算机学报.1999,22(10)：1105-1108.
[135]B. Johansson. On classification:simultaneously reducing dimensionality and finding automatic representation using canonical correlation. Technical report LiTH-ISY-R-2375, ISSN 1400-3902, Linkoping University,2001.
[136]A.M. Martinez and R. Benavente. (1998) The AR Face Database. CVC Technical Report, No.24.
[137]CASIA-PalmprintVl, http://www.cbsr.ia.ac.cn/PalmDatabase.htm.
[138]CASIA-IrisV3. http://www.cbsr.ia.ac.cn/IrisDatabase.htm.
[139]杨茂龙,孙权森,夏德深.2DCCA的实质与改进算法.解放军理工大学学报.2009,10(6)：517-522.
[140]李弼程,邵美珍,黄洁.模式识别原理与应用.西安：西安电子科技大学出版社,2008.
[141]Yoon Ho Bang, Chang Kyoo Yoo, In-Beum Lee. Nonlinear PLS modeling with fuzzy inference system. Chemometrics and Intelligent Laboratory Systems.2003,64: 137-155.
[142]Araby I. Abdel-Rahman, Gino J. Lim. A nonlinear partial least squares algorithm using quadratic fuzzy inference system. Journal of Chemometrics.2009,
[143]Moody J, Darken C. Fast learning in networks of locally-tuned processing units. Journal of Neural Computation.1989; 1:281-294.
[144]梁毅雄,龚卫国,潘英俊,李伟红,刘嘉敏,张红梅.基于奇异值分解的人脸识方法.光学精密工程,2004.10,12(5)：543-548.
[145]甘俊英,张有为.一种基于奇异值特征的神经网络人脸识别新途径.电子学报,2004.1,1：170-173.
[146]张贤达.矩阵分析与应用.第1版.北京：清华大学出版社,2006.
[147]班怀芸.基于模糊偏最小二乘分析的特征抽取技术.南京：南京理工大学硕士论文,2009.
[148]Wold S, Wold K, Skagerberg B. Nonlinear PLS modeling. Chem. Int. Lab. Sys. 1989.7:53-65.
[149]Roman Rosipal, Leonard J. Trejo. Kernel Partial Least Squares Regression in Reproducing Kernel Hilbert Space. Journal of Machine Learning Research.2001.2: 97-123.
[150]Bai Yifeng, Xiao Jian, Yu Long. Kernel Partial Least-Squares Regression.2006 International Joint Conference on Neural Networks, Sheraton Vancouver Wall Centre Hotel, Vancouver, BC, Canada,2006.
[151]Bart M. Nicolai, Karen I. Theron, Jeroen Lammertyn. Kernel PLS regression on wavelet transformed NIR spectra for prediction of sugar content of apple. Chemometrics and intelligent laboratory systems.2007.85:243-252.
[152]Long Han, Mark J. Embrechts, Yunqing Chen,etc. Kernel Partial Least Squares for the Identification of Mixture Content from TeraHertz Spectra.2006 International Joint Conference on Neural Networks Sheraton Vancouver Wall Centre Hotel, Vancouver, BC, Canada,2006.
[153]任建辉.基于核的非线性特征抽取与人脸识别方法研究.南京：南京理工大学硕士论文,2009.
[2]边肇祺,张学工.模式识别(第二版).北京：清华大学出版社,2000.
[3]John Shawe-Taylor, Nello Cristianini. Kernel Methods for Pattern Analysis. Cambridge University Press,2004.
[4]张学工译.统计学习理论的本质(第二版).北京：清华大学出版社,2000.
[5]李国正,王猛,曾华军等译.支持向量机导论.北京：电子工业出版社,2004.
[6]Liu C J, Wechsler H. A shape-and texture-based enhanced Fisher classifier for face recognition. IEEE Trans. Image Processing,2001,10(4):598-608.
[7]Yang J, Yang J Y. Generalized K-L transform based combined feature extraction. Pattern Recognition,2002,35(1):295-297.
[8]Yang J, Yang J Y, Zhang D, Lu J F. Yang J Y. Feature fusion:parallel strategy vs. serial strategy. Pattern Recognition,2003,36 (6):1369-1381.
[9]杨健.线性投影分析的理论与算法及其在特征抽取中的应用.南京：南京理工大学博士论文,2002.
[10]Yang J, Yang J Y, Frangi A F, Zhang D. Uncorrelated Projection Discriminant Analysis and Its Application to Face Image Feature Extraction. International Journal of Pattern Recognition and Artificial Intelligence,2003,17(8):1325-1347.
[11]Yang J, Zhang D, Xu Y, Yang J Y. Two-dimensional discriminant transform for face recognition. Pattern Recognition,2005,38(7):1125-1129.
[12]M. Borga, T. Landelius, H. Knutsson. A unified approach to PCA, PLS, MLR and CCA, Technical Report, LiTH-ISY-R-1992, Linkoping University, Sweden,1992.
[13]陆璇等译.实用多元统计分析(第四版).北京：清华大学出版社,2003.
[14]袁志发,周静芋.多元统计分析.北京：科学出版社,2002.
[15]James Lattin, J. Douglas Carroll, Paul E. Green. Analyzing Multivariate Data北京：机械工业出版社,2004.
[16]David G. Kleinbaum, Lawrence L.Kupper, Keith E. Muller, Azhar Nizam. Applied Regression Analysis and Other Multivariable Methods (Third Edition)北京：机械工业出版社,2006.
[17]孙权森.基于相关投影分析的特征抽取与图像识别研究.南京：南京理工大学博士论文,2006.
[18]孙挺凯.增强型典型相关分析研究与应用.南京：南京航空航天大学博士论文,2006.
[19]Long Han. kernel Partial Least Squares(K-PLS) for Scientific Data Mining. New York: Rensselaer Polytechnic Institute PHD thesis,2007.
[20]孙平,徐宗本,申建中.基于核化原理的非线性典型相关判别分析.计算机学报,2004,27(6)：789-795.
[21]Sun Q S, Zeng S G, Liu Y, Heng P A, Xia D S. A New Method of Feature Fusion and Its Application in Image Recognition. Pattern Recognition,2005,38(12):449-452.
[22]Sun Q S, Jin Z, Heng P A, Xia D S. A Novel Feature Fusion Method Based on Partial Least Squares Regression. The third International Conference on Advances in Pattern Recognition(Bath, UK, August 2005), Lecture Notes in Computer Science(LNCS), Springer-Verlag, Heidelberg, Berlin,2005,3686:268-277.
[23]Sun Q S, Liu Z D, Heng P A, Xia D S. A Theorem on the Generalized Canonical Projective Vectors. Pattern Recognition,2005,38(3):449-452.
[24]Sun Q S, Heng P A, Jin Z, Xia D S. Face Recognition Based on Generalized Canonical Correlation Analysis. International Conference on Intelligent Computing(Hefei, China, August 2005), Lecture Notes in Computer Science(LNCS), Springer-Verlag, Heidelberg, Berlin,2005,3645:958-967.
[25]孙权森,曾生根,王平安,夏德深.典型相关分析的理论及其在特征融合中的应用,计算机学报,2005,28(9)：1524-1533.
[26]孙权森,曾生根,杨茂龙,王平安,夏德深.基于典型相关分析的组合特征抽取及脸像鉴别,计算机研究与发展,2005,42(4)：614-621.
[27]M.Sargin, E. Erzin, Y. Yemez, et al. Multimodal speaker identification using canonical correlation analysis. IEEE International Conference on Acoustics, Speech and Signal Processing,2006(1):Ⅰ-613-Ⅰ-616.
[28]A. Pezeshki, A-Sadjadi, Scharf, et al. A canonical correlation-based feature extraction method for underwater target classification, Oceans'02 MTS/IEEE,2002 1:29-37.
[29]M. Hasan. A new approach for computing canonical correlations and coordinates. International Symposium on Circuits and Systems,2004,3:309-312.
[30]Nguyen D V, Rocke D M. Tumor classification by partial least squares using microarray gene expression data. Bioinformatics,2002,18(1):39-50.
[31]Nguyen D V, Rocke D M. Multi-class cancer classification via partial least squares with gene expression problems. Bioinformatics,2002,18(9):1216-1226.
[32]Nguyen D V, Rocke D M. Partial least squares proportional hazard regression for application to DNA microarraysurvival data. Bioinformatics,2002,18(12): 1625-1632.
[33]Miguel P E, Michel T. Prediction of clinical outcome with microarray data:a partial least squares discriminant analysis (PLS-DA) approach. Hum Genet,2003,112: 581-592.
[34]A. Nielsen. Multiset canonical correlations analysis and multispectral, truly multitemporal remote sensing data. IEEE Transactions on Image Processing,2002,11: 293-305.
[35]H. Ichihashi, K.Honda, S. Araki. Fuzzy canonical correlation and cluster analysis for brain mapping on long term memory consolidated by mnemonics. IEEE International Conference on Fuzzy Systems,2004,1(1):155-160.
[36]Y. Hel-Or, The canonical correlations of color images and their use for demosaicing, HP Labs Technical Report, HPL-2003-164(R.1), February 2004.
[37]Y. Yamanishi, J.-P. Vert, A. Nakayal, et al. Extraction of correlated gene clusters from multiple genomic data by generalized kernel canonical correlation analysis. Bioinformatics,2003,19(1), pp.i323-i330.
[38]M. Borga, H. Knutsson. A canonical correlation approach to blind source separation. Technical Report, LiU-IMT-EX-0062, Department of Biomedical Engineering, Linkoping University,2001.
[39]J. Galy, C. Adnet. Canonical correlation analysis:a blind source separation using non-circularity. Neural Networks for Signal Processing X, Proceedings of the 2000 IEEE Signal Processing Society Workshop,2000,1(11-13):465-473.
[40]M. Borga, O. Friman, P. Lundbergy, H. Knutsson. A canonical correlation approach to exploratory data analysis in fMRI. Proceedings of the ISMRM Annual Meeting, Honolulu, Hawaii,2002.
[41]J.K.Thomas, L.L.Scharf. Canonical correlations and canonical time series, IEEE International Conference on Acoustics, Speech, and Signal Processing,1996,3: 1637-1640.
[42]P. Schreier, L. Scharf, Canonical coordinates for transform coding of noisy sources, IEEE Transactions on signal processing,2006,54(1):235-243.
[43]M Kuss, T. Graepel. The geometry of kernel canonical correlation analysis. Max Planck Institute for Biological Cybernetics Technical Report No.108, May 2003.
[44]W. Zheng; X. Zhou; C. Zou et al. Facial expression recognition using kernel canonical correlation analysis (KCCA). IEEE Transactions on Neural Networks,2006,17(1): 233-238.
[45]A. Pezeshki, L. Scharf, Azimi-Sadjadi, et al. Empirical canonical correlation analysis in subspaces. Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers,2004,1:994-997.
[46]M. Loog, B. Ginneken, R.P.W. Duin. Dimensionality reduction of image features using the canonical contextual correlation projection. Pattern Recognition,2005,38(12): 2409-2418.
[47]P. Lai, S. Chuang, C Fyfe. Power load forecasting using neural canonical correlates. International Conference on Pattern Recognition,2000.
[48]T. Melzer, M. Reiter, H. Bischof, Appearance models based on kernel canonical correlation analysis, Pattern Recognition,2003,36(9):1961-1971.
[49]B. Fortuna. Kernel canonical correlation analysis with applications. In:SIKDD 2004 at Multiconference, Ljubljana, Slovenia.2004.
[50]D.R. Hardoon, S. Szedmak, J. Shawe-Taylor. Canonical correlation analysis:an overview with application to learning methods. Neural Computation 2004,16: 2639-2664.
[51]T. Gestel, J. Suykens, J. De Brabanter, et al. Kernel canonical correlation analysis and least squares support vector machines. In:Proc. of the International Conference on Artificial Neural Networks,2001,384-389.
[52]Y. He, L. Zhao, C. Zou. Face Recognition Based on PCA/KPCA plus CCA. In:L. Wang, K. Chen, and Y.S. Ong (Eds.):ICNC 2005, Berlin Heidelberg, Springer-Verlag, 2005, LNCS 3611, pp.71-74.
[53]S. Mika, G. Ratsch, J. Weston, B. Scholkopf, K-R. Muller. Fisher discriminant analysis with kernels. In:IEEE Neural Networks for Signal Processing Workshop,1999, 41-48.
[54]Matthew L. Barker. Partial least squares for discrimination. Lexington, Kentucky: University of Kentucky PHD thesis,2000.
[55]M. Yamada, A. Pezeshki, M. Azimi-Sadjadi. Relation between kernel CCA and kernel FDA. IEEE International Joint Conference on Neural Networks,2005,1(1):226-231.
[56]Colin Fyfe, Gayle Leen, Pei Ling Lai. Gaussian processes for canonical correlation analysis, Neurocomputing,2008 (71):3077-3088.
[57]Thomas Melzer. Generalized canonical correlation analysis for object recognition. [ph.D Dissertations], Vienna University of Technology,2002.
[58]M. Hasan. Information criteria for reduced rank canonical correlation analysis. IEEE International Joint Conference on Neural Networks,20043:2215-2220.
[59]P. Lai, C. Fyfe. Neural implementation of canonical correlation analysis. Neural Networks,1999,12(10):1391-1397.
[60]Y. Takane,Y. Oshima-Takane. Nonlinear generalized canonical correlation analysis by neural network models. In:Nishisato, S. et al. (Eds.), Measurement and Multivariate Analysis, Tokyo, Springer Verlag,2002, pp.183-190.
[61]X. Yin. Canonical correlation analysis based on information theory. Journal of Multivariate Analysis,2004,91(2):161-176.
[62]M. Barker, W. Rayens. Partial least squares for discrimination. Journal of Chemometrics,2003,17:166-173.
[63]Baek J, Kim M. Face recognition using partial least squares components. Pattern Recognition,2004,37(6):1303-1306.
[64]王惠文.偏最小二乘回归方法及其应用.北京：国防工业出版社,1999.
[65]王惠文,吴载斌,孟洁.偏最小二乘回归的线性与非线性方法.北京：国防工业出版社,2006.
[66]Vincenzo Esposito Vinzi, Michel Tenenhaus, Rong Guan. Proceedings of the 6th International Conference on Partial Least Squares and Related Methods. Beijing: Publishing House of Electronics Industry,2009.
[67]Du H Q, Ge H L et al. A new classifier for remote sensing data classification:partial least squares.2008 International Workshop on Earth Observation and Remote Sensing Applications.
[68]Kirby M, Sirovich L. Application of the K-L procedure for the characterization of human faces. IEEE Trans. Pattern Anal. Machine Intell.,1990,12(1):103-108.
[69]Turk M, Pentland A. Face processing:models for recognition. Proc. Intelligent Robots and Computer Vision Ⅷ, SPIE,1989,192:22-32.
[70]Turk M, Pentland A. Eigenfaces for recognition. J. Cognitive Neuroscience,1991,3(1): 71-86.
[71]Turk M, Pentland A. Face recognition using Eigenfaces. Proc. IEEE Conf. On Computer Vision and Pattern Recognition,1991,586-591.
[72]王建国.特征抽取方法研究及其在人脸识别中的应用.南京：南京理工大学博士论文,2008.
[73]Yang M H. Kernel Eigenfaces vs. Kernel Fisherfaces:Face Recognition Using Kernel Methods. Proceedings of the Fifth International Conference on Automatic Face and Gesture Recognition (FG), Washington D. C.,2002,215-220.
[74]金忠.人脸图像特征抽取与维数研究.南京：南京理工大学博士论文,1999.
[75]Jin Z, Yang J Y, Hu Z S, Lou Z. Face Recognition based on uncorrelated discriminant transformation. Pattern Recognition,2001,34(7):1405-1416.
[76]Jin Z, Yang J Y, Tang Z M, Hu Z S. A theorem on uncorrelated optimal discriminant vectors. Pattern Recognition,2001,34(10):2041-2047.
[77]Belhumeur P N, Hespanha J P, Kriegman D J. Eigenfaces vs. Fisherfaces:Recognition using class specific linear projection. IEEE Trans.Pattern Anal. Machine Intell.,1997, 19(7):711-720.
[78]Swets D L, Weng J. Using discriminant eigenfeatures for image retrieval. IEEE Trans. Pattern Anal. Machine Intell.,1996,18(8):831-836.
[79]杨健,杨静宇,叶晖.Fisher线性鉴别分析的理论及其应用.自动化学报,2003,29(4)：481-494.
[80]Hong Z Q, Yang J Y, et al. Optimal discriminant plane for a small number of samples and design method of classifier on the plane. Pattern Recognition,1991,24(4): 317-324.
[81]Liu K, Yang J Y, et al. An efficient algorithm for Foley-Sammon optimal set of discriminant vectors by algebraic method. International Journal of Pattern Recognition and Artificial Intelligence,1992,6(5):817-829.
[82]Guo G, et al. Face recognition by support vector machines. Proc.4th IEEE intern. Conf. Automatic Face and Gesture Recognition,2000,196-201.
[83]Guo Y F, Shu T T, Yang J Y. Feature extraction method based on the generalized Fisher Discriminant criterion and face recognition. Pattern Analysis & Application,2001, 4(1):61-66.
[84]Chen L F, Liao H M, Lin J C, Ko M T, Yu G J. A new LDA-based face recognition system which can solve the small sample size problem. Pattern Recognition,2000, 33(10):1713-1726.
[85]Hua Yu, Jian Yang, A direct LDA algorithm for high-dimensional data—with application to face recognition, Pattern Recognition.2001,34(11):2067-2070.
[86]杨健,杨静宇,金忠.最优鉴别特征的抽取及图像识别,计算机研究与发展,2001,38(11),pp.1331-1336.
[87]Kong H, Wang L, Teoh E K, Wang J G, Venkateswarlu R. A framework of 2D Fisher discriminant analysis:application to face recognition with small number of training samples. IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR),2005,2:1083-1088.
[88]严云洋.图像的特征抽取方法及其应用研究.南京：南京理工大学博士论文,2008.
[89]郭志波.人脸快速检测和特征抽取方法的研究.南京：南京理工大学博士论文,2007.
[90]Bartlett M.S., Movellan J.R., Sejnowski T.J. Face Recognition by Independent Component Analysis. IEEE Trans Neural Networks,2002.13(6):1450-1464.
[91]Liu C.J., Wechsler H. Independent component analysis of Gabor features for face recognition.2003,14(4):919-928.
[92]郭志波,杨静宇,刘华军.基于矩阵完备投影的快速主分量分析算法,中国图像图形学报,2007.12(4)：628-632.
[93]Hotelling H. Relations between two sets of variates. Biometrika,1936,8:321-377.
[94]Borga M. Learning Multidimensional Signal Processing. Linkoping Studies in Science and Technology, Dissertations, vol.531, Department of Electrical Engineering, Linkoping University, Linkoping, Sweden,1998.
[95]Tingkai Sun, Songcan Chen. Locality preserving CCA with applications to data visualization and pose estimation. Image and Vision Computing,2007,25(5):531-543.
[96]Grenier Y. Speaker adaptation through canonical correlation analysis. In:Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP,1980,5: 888-891.
[97]Choukri K, Chollet G, Grenier Y. Spectral transformations through canonical correlation analysis for speaker adptation in ASR. In:Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP,1986,2659-2662.
[98]Choi H C, King R W. Speaker adaptation through spectral transformation for HMM based speech recognition. IEEE International Symposium on Speech, Image Processing and Neural Networks,1994,2:686-689.
[99]Weenink D. Canonical Correlation Analysis. Institute of Phonetic Sciences, University of Amsterdam, Proceedings,2003,25:81-99.
[100]Bartlett M S. Further aspects of the theory of multiple regression. Proceedings of the Cambridge Philosophical Society,1938,34:33-40.
[101]L. Hoegaerts, J.A.K. Suykens, J. Vandewalle, B. De Moor. Subset based least squares subspace regression in RKHS. Elsevier Science,2004.
[102]Tingkai Sun, Songcan Chen. Class label versus sample label-based CCA. Applied Mathematics and Computation,2007,185(1):272-283.
[103]Yanyan Liu, Xiuping Liu, Zhixun Su. A new fuzzy approach for handling class labels in canonical correlation analysis. Neurocomputing,2008(71),1735-1740.
[104]Fu-Chang Liu, Jian Zhang, Quan-Sen Sun, De-Shen Xia. Generalized Canonical Correlation Analysis Using GSVD.2008 International Symposium on Computer Science and Computational Technology.200,136-141.
[105]Wold S, Martens H, Wold H. The Multivariate Calibration Problem in Chemistry Solved by the PLS Method. Proceedings of Conference on Matrix Pencils, Lecture Notes in Mathematics, Springer, Heidelberg,1983,286-293.
[106]Parthasarathy K, Jay H L, Victor S, Gopal A K. Partial least squares (PLS) based monitoring and control of batch digesters. Journal of Process Control,2000,10: 229-236.
[107]Yang Maolong, Mao Weihao, Sun Quansen, Xia Deshen. Sample labled-based PLS and feature extraction. Proceedings of the 6th International Conference on Partial Least Squares and Related Methods. Beijing:Publishing House of Electronics Industry. 2009,127-131.
[108]Jeronimo Arenas-Garcia, Gustavo Camps-Valls. Feature extraction from remote sensing data using kernel orthonormalized PLS.2007.
[109]Mattias Rantalainen, Max Bylesjo, etc. Kernel-based orthogonal projections to latent structures (K-OPLS). JOURNAL OF CHEMOMETRICS.2007; 21:376-385.
[110]孙宁等.基于2维偏最小二乘法的图像局部特征提取及其在面部表情识别中的应用.中国图像图形学报.2007,12(5),847-853.
[111]孙权森,陈强,夏德深.基于偏最小二乘分析的人脸表示与识别.江南大学学报.2008,7(1),1-5.
[112]Svante Wold, Johan Trygg, Anders Berglund, Henrik Antti. Some recent developments in PLS modeling. Chemometrics and Intelligent Laboratory Systems. 2001,58,131-150.
[113]Svante Wold, Michael Sjostrom, Lennart Eriksson. PLS-regression:a basic tool of chemometrics.Chemometrics and Intelligent Laboratory Systems.2001,58,109-130.
[114]Svante Wold. Personal memories of the early PLS development. Chemometrics and Intelligent Laboratory Systems.2001(58):83-84.
[115]Yushu Liu, William Rayens. PLS and dimension reduction for classification.Computational Statistics.2007(22),189-208.
[116]Max Bylesjo, Mattias Rantalainen, Olivier Cloarec, Jeremy K. Nicholson, Elaine Holmesand Johan Trygg. OPLS discriminant analysis:combining the strengths of PLS-DA and SIMCA classification. Journal of Chemometrics 2006(20):341-351.
[117]A.Hoskuldsson PLS Regression Methods. Journal of Chemometrics,1988,2: 211-228.
[118]A.Hoskuldsson Causal and path modeling. Chemometrics and Intelligent Laboratory Systems,2001,58:287-311.
[119]Liu K, Cheng Y Q, Yang J Y. Algebraic feature extraction for image recognition based on an optimal discriminant criterion. Pattern Recognition,1993,26 (6): 903-911.
[120]Yang Jian, Zhang David, Yang Jingyu. Two-dimensional PCA:a new approach to appearance-based face representation and recoginition. Pattern Analysis and Machine Intelligence.2004,26 (1):131-137.
[121]Wang Liwei, Wang Xiao, Zhang Xuerong, et al. The equivalence of two dimensional PCA and line-based PCA. Pattern Recognition Letters.2005,26(1):57-60.
[122]徐勇,杨健,赵英男,宋枫溪,杨静宇.一种缩减图像维数的方法及其在人脸图像上的应用.电子与信息学报.2008,30(1)：180-184.
[123]张生亮,谢永华,杨静宇.一种双向压缩的二维特征抽取算法及其应用.计算机应用研究.2006,23(5)：63-69.
[124]Sun Ho Lee, Seungjin Choi. Two-dimensional canonical correlation analysis. IEEE Signal Processing Letters.2007,14(10):1-4.
[125]Cai-rong Zou, Ning Sun, Zhen-hai Ji, Li Zhao.2DCCA:a novel method for small sample size face recognition. IEEE Workshop on Applications of Computer Vision(WACV07).2007,149-154.
[126]周晓彦,郑文明,赵力,邹采荣.基于偏最小二乘回归的人脸身份和表情同步识别方法.中国图象图形学报.2009,14(5)：801-808.
[127]Mao-long Yang, Quan-sen Sun, De-shen Xia. Two-dimensional partial squares and its application in image recognition. Proceedings of the 4th International Conference on Intelligence Computing (ICIC'08).2008,208-215.
[128]Yang Maolong, Mao Weihao, Sun Quansen, Xia Deshen. Combine Feature Extraction of Palmprint and Face Images Based on PLS. Proceedings of the 6th International Conference on Partial Least Squares and Related Methods. Beijing: Publishing House of Electronics Industry.2009,324-131.
[129]Ben Niu, Qiang Yang, et al. Two-dimensional laplacianfaces method for face recognition. Pattern Recognition.2007.
[130]Dewen Hu, Guiyu Feng, Zongtan Zhou. Two-dimensional locality preserving projections (2DLPP) with its application to palmprint recognition. Pattern Recognition. 2007,40:339-342.
[131]Sibao Chen, Haifeng Zhao, Min Kong, Bin Luo.2D-LPP:A two-dimensional extension of locality preserving projections. Neurocomputing.2007,70:912-921.
[132]Xin Pan, Qiu-Qi Ruan. Palmprint recognition with improved two-dimensional locality preserving projections. Image and Vision Computing.2008.
[133]张润楚.多元统计分析.北京：科学出版社,2007.
[134]金钟,杨静宇,陆建峰.一种具有统计不相关性的最佳鉴别矢量集.计算机学报.1999,22(10)：1105-1108.
[135]B. Johansson. On classification:simultaneously reducing dimensionality and finding automatic representation using canonical correlation. Technical report LiTH-ISY-R-2375, ISSN 1400-3902, Linkoping University,2001.
[136]A.M. Martinez and R. Benavente. (1998) The AR Face Database. CVC Technical Report, No.24.
[137]CASIA-PalmprintVl, http://www.cbsr.ia.ac.cn/PalmDatabase.htm.
[138]CASIA-IrisV3. http://www.cbsr.ia.ac.cn/IrisDatabase.htm.
[139]杨茂龙,孙权森,夏德深.2DCCA的实质与改进算法.解放军理工大学学报.2009,10(6)：517-522.
[140]李弼程,邵美珍,黄洁.模式识别原理与应用.西安：西安电子科技大学出版社,2008.
[141]Yoon Ho Bang, Chang Kyoo Yoo, In-Beum Lee. Nonlinear PLS modeling with fuzzy inference system. Chemometrics and Intelligent Laboratory Systems.2003,64: 137-155.
[142]Araby I. Abdel-Rahman, Gino J. Lim. A nonlinear partial least squares algorithm using quadratic fuzzy inference system. Journal of Chemometrics.2009,
[143]Moody J, Darken C. Fast learning in networks of locally-tuned processing units. Journal of Neural Computation.1989; 1:281-294.
[144]梁毅雄,龚卫国,潘英俊,李伟红,刘嘉敏,张红梅.基于奇异值分解的人脸识方法.光学精密工程,2004.10,12(5)：543-548.
[145]甘俊英,张有为.一种基于奇异值特征的神经网络人脸识别新途径.电子学报,2004.1,1：170-173.
[146]张贤达.矩阵分析与应用.第1版.北京：清华大学出版社,2006.
[147]班怀芸.基于模糊偏最小二乘分析的特征抽取技术.南京：南京理工大学硕士论文,2009.
[148]Wold S, Wold K, Skagerberg B. Nonlinear PLS modeling. Chem. Int. Lab. Sys. 1989.7:53-65.
[149]Roman Rosipal, Leonard J. Trejo. Kernel Partial Least Squares Regression in Reproducing Kernel Hilbert Space. Journal of Machine Learning Research.2001.2: 97-123.
[150]Bai Yifeng, Xiao Jian, Yu Long. Kernel Partial Least-Squares Regression.2006 International Joint Conference on Neural Networks, Sheraton Vancouver Wall Centre Hotel, Vancouver, BC, Canada,2006.
[151]Bart M. Nicolai, Karen I. Theron, Jeroen Lammertyn. Kernel PLS regression on wavelet transformed NIR spectra for prediction of sugar content of apple. Chemometrics and intelligent laboratory systems.2007.85:243-252.
[152]Long Han, Mark J. Embrechts, Yunqing Chen,etc. Kernel Partial Least Squares for the Identification of Mixture Content from TeraHertz Spectra.2006 International Joint Conference on Neural Networks Sheraton Vancouver Wall Centre Hotel, Vancouver, BC, Canada,2006.
[153]任建辉.基于核的非线性特征抽取与人脸识别方法研究.南京：南京理工大学硕士论文,2009.