人脸识别中基于流形学习的特征提取方法研究
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摘要
人脸识别以其自然、直接、非接触、安全等优点发展为最具潜力的生物特征识别技术，它利用人脸面部特征中的有效信息进行个人身份识别。由于人脸识别在身份验证和识别场合具有巨大的应用价值，以及能促进模式识别等多门学科的发展。因此，对人脸识别技术的研究具有重大的理论和实际意义。
提取有效的鉴别特征是人脸识别的一个关键因素，它要求在保持人脸数据集原有的本质结构特性不变的同时进行数据维数约减。流形学习作为一种非线性的维数约减方法，能够有效地学习出高度非线性、属性强相关的高维流形数据的内在几何结构。本文在对基于流形学习的特征提取方法进行深入研究的基础上，主要做了以下工作：
1.在邻域保持判别嵌入的基础上，将核映射的思想进行引入其中，并在特征值求解时以Schur正交方式找出最优投影向量，提出了核正交邻域保持判别嵌入算法，克服了邻域保持判别嵌入难以提取非线性特征的困难，很好地保持了人脸流形的几何结构和判别结构信息。
2.监督算法和无监督算法都不能充分利用有限的训练样本。因此，本文将无监督判别分析和边界Fisher分析进行结合，改进为半监督算法。其中，利用无监督判别分析来对大量无标签样本进行学习，而利用边界Fisher分析对少量有标签样本进行学习。同时，采用最大散度差准则作为目标函数，避免了散度矩阵奇异值的产生，通过理论分析和实验验证了该方法的可行性和有效性。
3.张量边界Fisher分析直接采用图像进行维数约减，避免了传统的方法将图像展开为一维向量的形式，更有效地保持了人脸结构信息。然而在构建最近邻图时，张量边界Fisher分析采用全局统一的k邻域法来选择近邻点的，对于非均匀流形的处理比较困难。本文在研究以上算法的基础上，采用测地距离与欧氏距离的关系来动态的选择训练样本近邻点，使得更有效地选取适合每个样本的局部线性或近似线性区域。
Face recognition, characterizing by its naturalness, directness, non-contact,securit, etc., has developed to be a most potential biometric identification technology.The effective information of the facial features is utilized for personal identification.Face recognition has tremendous using value in authentication and identify occasions,and can promote the development of pattern recognition and many other subjects.Therefore, the study of face recognition technology is great theoretical and practicalsignificance.
Extract effective discriminant features is a key factor in face recognition, whichrequires reduction of the data dimensionat and keep the face data set of the originalnature of structural characteristics unchanging at the same time. As non-lineardimension reduction methods, manifold learning can effectively learn the intrinsicgeometry of the high-dimensional manifold data structure closely related to highnonlinearity and properties. In this paper, based on the deeply inveatigation of featureextraction method based on manifold learning, the main contents and innovations arelisted as follows:
Firstly, on the basis of Neighborhood Preserving Discriminant Embedded (NPDE),introducing the idea of Kernel mapping, finding the optimal projection vector usingSchur orthogonal way while solving the eigenvalue, proposing the Kernel OrthogonalNeighborhood Preserving Discriminant Embedding (KONPDE), overcoming theproblem that NPDE is hard to extract nonlinear characteristics, well maintaining theinformation of geometry and the discriminant of structural information of the facemanifold.
Secondly, supervision algorithm and unsupervised algorithm can not make fulluse of limited training samples. Therefore, the Unsupervised Discrimination Projection(UDP) and Marginal Fisher Analysis (MFA) are combined to improve to besemi-supervised algorithm. There among, a large number of label-free samples arestudied using UDP, a small number of label samples are investigated using the MFA.At the same time, choose the maximum scatter difference criterion as the objectivefunction to avoid the divergence matrix singular value, verify the feasibility andeffectiveness of the method through theoretical and experimental alanalysis.
Finally, the Tensor Marginal Fisher Analysis (TMFA) use image dimensionalityreduction to avoid that the traditional method expands the image in the form of a one-dimensional vector, which is effectively keep the face structure information.However, when building a nearest neighbor diagram, TMFA employ the global unifiedk-neighborhood method to select a close neighbor of the point, which is more difficultfor non-uniform flow shape processing. On the basis of the above algorithm in theresearch, the method that adopting the relationship between the euclidean distance andthe geodesic distance to select training samples nearest neighbor points dynamically isproposed, which makes it more effective to select local linear or nearly linear regionfor each sample.
提取有效的鉴别特征是人脸识别的一个关键因素，它要求在保持人脸数据集原有的本质结构特性不变的同时进行数据维数约减。流形学习作为一种非线性的维数约减方法，能够有效地学习出高度非线性、属性强相关的高维流形数据的内在几何结构。本文在对基于流形学习的特征提取方法进行深入研究的基础上，主要做了以下工作：
1.在邻域保持判别嵌入的基础上，将核映射的思想进行引入其中，并在特征值求解时以Schur正交方式找出最优投影向量，提出了核正交邻域保持判别嵌入算法，克服了邻域保持判别嵌入难以提取非线性特征的困难，很好地保持了人脸流形的几何结构和判别结构信息。
2.监督算法和无监督算法都不能充分利用有限的训练样本。因此，本文将无监督判别分析和边界Fisher分析进行结合，改进为半监督算法。其中，利用无监督判别分析来对大量无标签样本进行学习，而利用边界Fisher分析对少量有标签样本进行学习。同时，采用最大散度差准则作为目标函数，避免了散度矩阵奇异值的产生，通过理论分析和实验验证了该方法的可行性和有效性。
3.张量边界Fisher分析直接采用图像进行维数约减，避免了传统的方法将图像展开为一维向量的形式，更有效地保持了人脸结构信息。然而在构建最近邻图时，张量边界Fisher分析采用全局统一的k邻域法来选择近邻点的，对于非均匀流形的处理比较困难。本文在研究以上算法的基础上，采用测地距离与欧氏距离的关系来动态的选择训练样本近邻点，使得更有效地选取适合每个样本的局部线性或近似线性区域。
Face recognition, characterizing by its naturalness, directness, non-contact,securit, etc., has developed to be a most potential biometric identification technology.The effective information of the facial features is utilized for personal identification.Face recognition has tremendous using value in authentication and identify occasions,and can promote the development of pattern recognition and many other subjects.Therefore, the study of face recognition technology is great theoretical and practicalsignificance.
Extract effective discriminant features is a key factor in face recognition, whichrequires reduction of the data dimensionat and keep the face data set of the originalnature of structural characteristics unchanging at the same time. As non-lineardimension reduction methods, manifold learning can effectively learn the intrinsicgeometry of the high-dimensional manifold data structure closely related to highnonlinearity and properties. In this paper, based on the deeply inveatigation of featureextraction method based on manifold learning, the main contents and innovations arelisted as follows:
Firstly, on the basis of Neighborhood Preserving Discriminant Embedded (NPDE),introducing the idea of Kernel mapping, finding the optimal projection vector usingSchur orthogonal way while solving the eigenvalue, proposing the Kernel OrthogonalNeighborhood Preserving Discriminant Embedding (KONPDE), overcoming theproblem that NPDE is hard to extract nonlinear characteristics, well maintaining theinformation of geometry and the discriminant of structural information of the facemanifold.
Secondly, supervision algorithm and unsupervised algorithm can not make fulluse of limited training samples. Therefore, the Unsupervised Discrimination Projection(UDP) and Marginal Fisher Analysis (MFA) are combined to improve to besemi-supervised algorithm. There among, a large number of label-free samples arestudied using UDP, a small number of label samples are investigated using the MFA.At the same time, choose the maximum scatter difference criterion as the objectivefunction to avoid the divergence matrix singular value, verify the feasibility andeffectiveness of the method through theoretical and experimental alanalysis.
Finally, the Tensor Marginal Fisher Analysis (TMFA) use image dimensionalityreduction to avoid that the traditional method expands the image in the form of a one-dimensional vector, which is effectively keep the face structure information.However, when building a nearest neighbor diagram, TMFA employ the global unifiedk-neighborhood method to select a close neighbor of the point, which is more difficultfor non-uniform flow shape processing. On the basis of the above algorithm in theresearch, the method that adopting the relationship between the euclidean distance andthe geodesic distance to select training samples nearest neighbor points dynamically isproposed, which makes it more effective to select local linear or nearly linear regionfor each sample.
引文
[1]王国强.嵌入邻域判别关系的子空间人脸识别算法研究[博士学位论文].大连:大连理工大学,2008.
[2] Starovoitov V, Samal D. A geometric approach to face recognition[C]. Proc of theIEEE-EURASIP Workshop on sNonlinear Signal and Image Processing, Antalya,Turkey,1999,1:210-213.
[3] Howell A J, Buxton H. Learning identity with radial basis function networks[J].Neurocomputing,1998,20:15-34.
[4] Guo G, Li S Z, Chan K. Face Recognition by Support Vector Machines[C]. Proc ofFourth IEEE International Conference on Automatic Face and GestureRecognition, Grenoble,2000:196-201.
[5] Freund Y, Schapire R E. A decision-theoretic generalization of on-1ine learningand application to boosting[C]. Proc of the2th European Conference onComputational Learning Theory. Germany, Springer Verlag,1995:23-37.
[6] Wiskott L, Fellous J M, Kruger N, et al. Face recognition by elastic bunch graphmatching[J]. Pattern Anaysis and Machine Intelligence,1997,19(7):775-779.
[7] Xiao J, Kanade T. Non-rigid shape and motion recovery: degrenerate[C]. Proc ofthe2004IEEE Conference on ComputerVision and Pattern Recognition.Washington DC, USA,2004:668-675.
[8]刘青山,卢汉清.综述人脸识别中的子空间方法[J].自动化学报,2003,29(6):900-911.
[9] Rao A, Noushath S. Subspace methods for face recognition[J]. Computer ScienceReview,2010,4(1):1-17.
[10] Turk M, Pentland A. Eigenfaces for Recognition[J]. Journal of CognitiveNeuroscience,1991,3(1):71-86.
[11] Yang J, David Z, Alejandro F. Frangi, et al. Two-Dimensional PCA: a NewApproach to Face Representation and Recognition[J]. Pattern analysis andmachine intelligence,2004,26(1):131-137.
[12] Scholkopf B, Smola A, Muller K R. Nonlinear Component Analysis as a KernelEigenvalue Problem[J]. Neural Computation,2006,10(5):1229-1319.
[13] Belhumeur P, Hespanha J, Kriegman D. Eigenfaces VS. Fisherfaces:Recognitionusing class specific1inear projection[J]. Pattern Analysis and MachineIntelligence,1997,19(7):711-720.
[14] Zhao W, Chellappa R, Krishnaswamy A. Discriminant analysis of Principalcomponents for face recognition[C]. Proc of the2nd International Conferece onAutomatic Facerecognition, Nara,1998:336-341.
[15] Yu H, Yang J. A direct LDA algorithm for high dimensional data with applicationto face recognition[J]. Pattern Recognition,2000,34(10):2067-2070.
[16]刘永俊,陈才扣.最大散度差鉴别分析及人脸识别[J].计算机工程与应用,2006,34:208-210.
[17] Bartlett M S, Movellan J R, Sejnowski T J. Face recognition by independentcomponent analysis[J]. IEEE Transactions on Neural Networks,2002,13(6):1450-1464.
[18]刘青山,黄睿.基于核Fisher鉴别分析的人脸识别[J].计算机学报,2002,21(5):89-96.
[19] Tenenbaum J B, De S V, Langford J C. A global geometric framework fornonlinear dimensionality reduction[J]. Science,2000,290(5500):2319-2323.
[20] Roweis S L, Saul L. Nonlinear dimensionality reduction by locally linearembedding[J]. Science,2000,290(5500):2323-2326.
[21] Belkin M, Niyogi P. Laplacian eigenmaps for dimensionality reduction and datarepresentation[J]. Neural Computation,2003,15(6):1373-1396.
[22] He X F, Niyogi P. Locality preserving projections[C]. Proc of Advances in NeuralInformation Processing Systems. Camb ridge,2004:153-160.
[23] Xu Y, Zhong A N, Yang J. LPP solution schemes for use with face recognition[J].Pattern Recognition,2010,43(12):4165-4176.
[24] Yang J, David Z. Globally maximizing, locally minimizing:unsuperviseddiscriminant projection with applications to face and palm biometrics[J].IEEETrans Pattern Anal Machine Intell,2007,29(4):650-664.
[25] He X F, Cai D, Yan S C, et al. Neighborhood Preserving Embedding[C] Proc ofInternational Conference on Computer Vision. Beijing, China,2005:1208-1213.
[26] Qiu X, Wu L. Face recognition by stepwise nonparametric margin maximumcriterion [C]. Proc of the Tenth IEEE International Conference on ComputerVision. Beijing, China,2005:1567-1572.
[27] Cai D, He X F. Locality sensitive discriminate analysis[C]. Proc of the20thinternational joint conference on Artifical intelligence, San Francisco, USA,2007:708-713.
[28] Li B, Zheng C H, Huang D S. Locally linear discriminant embedding: An efficientmethod for face recognition[J]. Pattern Recognition,2008,41(12):3813-3821.
[29] Sugiyama M, Ide T, Nakajima S, et al. Semi-Supervised Local Fisher DiscriminantAnalysis for Dimensionality Reduction[J]. Machine Learning,2008,78(1):35-61.
[30] Song Y Q, Nie F P, Zhang C S, et al. A Unified Framework for Semi-SupervisedDimensionality Reduction [J]. Pattern Recognition,2008,41:2789-2799.
[31] Zhang S W, Lei Y K, Wu Y H. Semi-supervised locally discriminant projection forclassification and recognition[J]. Knowledge-Based Systems,2011,24(2):341-346.
[32] Cai D, He X F, Han J W. Semi-supervised discriminant analysis[C]. Proc of the11th IEEE International Conference on Computer Vision. Riode Janeim,2007:1-7.
[33] Qiu H N, Lai J H, Huang J, et al. Semi-supervised discriminant analysis based onUDP regularization[C]. Proc of the19th International Conference on PatternRecognition. Tampa,2008:1-4.
[34] He X, Cai D, Nigygi P. Tensor subspace analysis[OL]. http://books.nips.cc/nips18.html,2007-10-20.
[35] Xu D, Yan S, Tao D, et al. Marginal fisher analysis and its variants for human gaitrecognition and content based image retrieval[J]. IEEE Transactions on ImageProcessing,2007,16(11):2811-2821.
[36]庞彦伟,俞能海,沈道义,等.基于核邻域保持投影的人脸识别[J].电子学报,2006,34(8):1542-1544.
[37]黄启宏,刘钊.流形学习中非线性维数约简方法概述[J].计算机应用研究,2007,24(11):19-25.
[38]周红,吴炜,滕奇志.流形学习中的算法研究[J].计算机应用研究,2007,24(7):214-217.
[39]李勇周.人脸识别中基于流形学习的子空间特征提取方法研究[博士学位论文].长沙:中南大学,2009.
[40] Pang Y H, Andrew T B J, Fazly S A. Neighbourhood preserving discriminantembedding in face recognition [J]. Journal of Visual Communication and ImageRepresentation,2009,20(8):532-542.
[41]杜海顺,柴秀丽,汪凤泉,等.一种邻域保持判别嵌入人脸识别方法[J].仪器仪表学报,2010,31(3):625-629.
[42]曹丽.基于流形的特征抽取及人脸识别研究[硕士学位论文].扬州:扬州大学,2009.
[43] Cai D, He X F, Han J, et al. Orthogonal Laplacianfaces for face recognition[J].IEEE Transactions Image Processing,2006，15(11):3608-3614.
[44]刘慧,袁文燕.矩阵论及其应用[M].北京:化学工业出版社,2003.
[45] Chatpatanasiri R, Kijsirikul B. A unified semi-supervised dimensionality reductionframework for manifold learning[J]. Neurocomputing,2010,73(10):1631-1640.
[46] Zhang D Q, Zhou Z H, Chen S C. Semi-Supervised Dimensionality Reduction[C].Proc of the7th SIAM International Conference on Data Mining,2007:191-203.
[47] Huang H, Li J W, Liu J M. Enhanced semi-supervised local Fisher discriminantanalysis for face recognition[J]. Future Generation Computer Systems,2012,28(1):244-253.
[48]卢桂馥,林忠,金忠.基于最大差值的二维边界Fisher的人脸识别[J].计算机科学,2010,37(5):775-779.
[49] Li M, Yuan B Z.2D-LDA: a statistical linear discriminant analysis for imagematrixv[J]. Pattern Recognition Letter,2005,26(5):527-532.
[50]文贵华,江丽君,文军.邻域参数动态变化的局部线性嵌入[J].软件学报,2008,19(7):1666-1673.
[51]詹宇斌,殷建平,刘新旺,等.流形学习中基于局部线性结构的自适应邻域选择[J].计算机研究与发展,2011,48(4):576-583.
[2] Starovoitov V, Samal D. A geometric approach to face recognition[C]. Proc of theIEEE-EURASIP Workshop on sNonlinear Signal and Image Processing, Antalya,Turkey,1999,1:210-213.
[3] Howell A J, Buxton H. Learning identity with radial basis function networks[J].Neurocomputing,1998,20:15-34.
[4] Guo G, Li S Z, Chan K. Face Recognition by Support Vector Machines[C]. Proc ofFourth IEEE International Conference on Automatic Face and GestureRecognition, Grenoble,2000:196-201.
[5] Freund Y, Schapire R E. A decision-theoretic generalization of on-1ine learningand application to boosting[C]. Proc of the2th European Conference onComputational Learning Theory. Germany, Springer Verlag,1995:23-37.
[6] Wiskott L, Fellous J M, Kruger N, et al. Face recognition by elastic bunch graphmatching[J]. Pattern Anaysis and Machine Intelligence,1997,19(7):775-779.
[7] Xiao J, Kanade T. Non-rigid shape and motion recovery: degrenerate[C]. Proc ofthe2004IEEE Conference on ComputerVision and Pattern Recognition.Washington DC, USA,2004:668-675.
[8]刘青山,卢汉清.综述人脸识别中的子空间方法[J].自动化学报,2003,29(6):900-911.
[9] Rao A, Noushath S. Subspace methods for face recognition[J]. Computer ScienceReview,2010,4(1):1-17.
[10] Turk M, Pentland A. Eigenfaces for Recognition[J]. Journal of CognitiveNeuroscience,1991,3(1):71-86.
[11] Yang J, David Z, Alejandro F. Frangi, et al. Two-Dimensional PCA: a NewApproach to Face Representation and Recognition[J]. Pattern analysis andmachine intelligence,2004,26(1):131-137.
[12] Scholkopf B, Smola A, Muller K R. Nonlinear Component Analysis as a KernelEigenvalue Problem[J]. Neural Computation,2006,10(5):1229-1319.
[13] Belhumeur P, Hespanha J, Kriegman D. Eigenfaces VS. Fisherfaces:Recognitionusing class specific1inear projection[J]. Pattern Analysis and MachineIntelligence,1997,19(7):711-720.
[14] Zhao W, Chellappa R, Krishnaswamy A. Discriminant analysis of Principalcomponents for face recognition[C]. Proc of the2nd International Conferece onAutomatic Facerecognition, Nara,1998:336-341.
[15] Yu H, Yang J. A direct LDA algorithm for high dimensional data with applicationto face recognition[J]. Pattern Recognition,2000,34(10):2067-2070.
[16]刘永俊,陈才扣.最大散度差鉴别分析及人脸识别[J].计算机工程与应用,2006,34:208-210.
[17] Bartlett M S, Movellan J R, Sejnowski T J. Face recognition by independentcomponent analysis[J]. IEEE Transactions on Neural Networks,2002,13(6):1450-1464.
[18]刘青山,黄睿.基于核Fisher鉴别分析的人脸识别[J].计算机学报,2002,21(5):89-96.
[19] Tenenbaum J B, De S V, Langford J C. A global geometric framework fornonlinear dimensionality reduction[J]. Science,2000,290(5500):2319-2323.
[20] Roweis S L, Saul L. Nonlinear dimensionality reduction by locally linearembedding[J]. Science,2000,290(5500):2323-2326.
[21] Belkin M, Niyogi P. Laplacian eigenmaps for dimensionality reduction and datarepresentation[J]. Neural Computation,2003,15(6):1373-1396.
[22] He X F, Niyogi P. Locality preserving projections[C]. Proc of Advances in NeuralInformation Processing Systems. Camb ridge,2004:153-160.
[23] Xu Y, Zhong A N, Yang J. LPP solution schemes for use with face recognition[J].Pattern Recognition,2010,43(12):4165-4176.
[24] Yang J, David Z. Globally maximizing, locally minimizing:unsuperviseddiscriminant projection with applications to face and palm biometrics[J].IEEETrans Pattern Anal Machine Intell,2007,29(4):650-664.
[25] He X F, Cai D, Yan S C, et al. Neighborhood Preserving Embedding[C] Proc ofInternational Conference on Computer Vision. Beijing, China,2005:1208-1213.
[26] Qiu X, Wu L. Face recognition by stepwise nonparametric margin maximumcriterion [C]. Proc of the Tenth IEEE International Conference on ComputerVision. Beijing, China,2005:1567-1572.
[27] Cai D, He X F. Locality sensitive discriminate analysis[C]. Proc of the20thinternational joint conference on Artifical intelligence, San Francisco, USA,2007:708-713.
[28] Li B, Zheng C H, Huang D S. Locally linear discriminant embedding: An efficientmethod for face recognition[J]. Pattern Recognition,2008,41(12):3813-3821.
[29] Sugiyama M, Ide T, Nakajima S, et al. Semi-Supervised Local Fisher DiscriminantAnalysis for Dimensionality Reduction[J]. Machine Learning,2008,78(1):35-61.
[30] Song Y Q, Nie F P, Zhang C S, et al. A Unified Framework for Semi-SupervisedDimensionality Reduction [J]. Pattern Recognition,2008,41:2789-2799.
[31] Zhang S W, Lei Y K, Wu Y H. Semi-supervised locally discriminant projection forclassification and recognition[J]. Knowledge-Based Systems,2011,24(2):341-346.
[32] Cai D, He X F, Han J W. Semi-supervised discriminant analysis[C]. Proc of the11th IEEE International Conference on Computer Vision. Riode Janeim,2007:1-7.
[33] Qiu H N, Lai J H, Huang J, et al. Semi-supervised discriminant analysis based onUDP regularization[C]. Proc of the19th International Conference on PatternRecognition. Tampa,2008:1-4.
[34] He X, Cai D, Nigygi P. Tensor subspace analysis[OL]. http://books.nips.cc/nips18.html,2007-10-20.
[35] Xu D, Yan S, Tao D, et al. Marginal fisher analysis and its variants for human gaitrecognition and content based image retrieval[J]. IEEE Transactions on ImageProcessing,2007,16(11):2811-2821.
[36]庞彦伟,俞能海,沈道义,等.基于核邻域保持投影的人脸识别[J].电子学报,2006,34(8):1542-1544.
[37]黄启宏,刘钊.流形学习中非线性维数约简方法概述[J].计算机应用研究,2007,24(11):19-25.
[38]周红,吴炜,滕奇志.流形学习中的算法研究[J].计算机应用研究,2007,24(7):214-217.
[39]李勇周.人脸识别中基于流形学习的子空间特征提取方法研究[博士学位论文].长沙:中南大学,2009.
[40] Pang Y H, Andrew T B J, Fazly S A. Neighbourhood preserving discriminantembedding in face recognition [J]. Journal of Visual Communication and ImageRepresentation,2009,20(8):532-542.
[41]杜海顺,柴秀丽,汪凤泉,等.一种邻域保持判别嵌入人脸识别方法[J].仪器仪表学报,2010,31(3):625-629.
[42]曹丽.基于流形的特征抽取及人脸识别研究[硕士学位论文].扬州:扬州大学,2009.
[43] Cai D, He X F, Han J, et al. Orthogonal Laplacianfaces for face recognition[J].IEEE Transactions Image Processing,2006，15(11):3608-3614.
[44]刘慧,袁文燕.矩阵论及其应用[M].北京:化学工业出版社,2003.
[45] Chatpatanasiri R, Kijsirikul B. A unified semi-supervised dimensionality reductionframework for manifold learning[J]. Neurocomputing,2010,73(10):1631-1640.
[46] Zhang D Q, Zhou Z H, Chen S C. Semi-Supervised Dimensionality Reduction[C].Proc of the7th SIAM International Conference on Data Mining,2007:191-203.
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