随机增量张量奇异值分解与人脸识别新算法
|
摘要
本文新提出随机增量张量奇异值分解方法.当数据逐步增加时,新方法能够在保持原数据的随机奇异值分解基础上,通过计算新增数据的奇异值分解得到更新后数据的张量奇异值分解.基于随机增量张量奇异值分解建立新的人脸识别模型.数值实验表明新模型与已有人脸识别模型相比具有较高的识别率.
In this paper,the randomized tensor singular value decomposition with increment is proposed.In the process of updating the training datasets,the existing results of the original datasets can be maintained and utilized to obtain the SVD decomposition of the new datasets.Based on the randomized tensor singular value decomposition with increment,a new model of face recognition is established.Numerical experiments show that the new model has higher recognition rate than existing face recognition models.
In this paper,the randomized tensor singular value decomposition with increment is proposed.In the process of updating the training datasets,the existing results of the original datasets can be maintained and utilized to obtain the SVD decomposition of the new datasets.Based on the randomized tensor singular value decomposition with increment,a new model of face recognition is established.Numerical experiments show that the new model has higher recognition rate than existing face recognition models.
引文
[1]韩玉峰,王小林,张传文.生物特征识别技术研究及应用[J].微计算机信息,2012(3):33-35.
[2]Karl Pearson.On lines and planes of cloest fit to systems of points in space[J].Philosophical Magazine,1901(2):559-572.
[3]马小龙.数据降维方法综述[D].北京:清华大学,2005.
[4]Yang J,Zhang D,Frangi A F,et al.Two-dimensional PCA:a new approach to appearance based face representation and recognition[J].IEEE Trans on Patten Analysis and Machine Intelligence,2004,26(1):131-137.
[5]Li M,Yuan B Z.2D-LDA:A statistical linear discriminant analysis for image matrix[J].Pattern Recognition Letters,2005,26(5):527-532.
[6]Yan S C,Xu D,Yang Q,et al.Multilinear discriminant analysis for face recognition[J].IEEE Trans on Image Processing,2007,16(1):212-220.
[7]Kolda T G,Bader B W.Tensor decompositions and applications[J].Siam Review,2009,51(3):455-500.
[8]Carroll J D,Chang J.Analysis of individual differences in multidimensional scaling via an n-way generalization of“eckart-young”decomposition[J].Psychometrika,1970,35(3):283-319.
[9]Tucker L R.Some mathematical notes on three-mode factor analysis[J].Psychometrika,1966,31(3):279-311.
[10]Lathauwer L D,Moor B D,Vandewalle J.A multilinear singular value decomposition[J].SIAM Journal of Matrix Analysis and Applications,2000,21(4):1253-1278.
[11]Kilmer M E,Martin C D.Factorization strategies for third-order tensors[J].Linear Algebra and Its Applications,2011,435(3):641-658.
[12]Vasilescu M A O,Terzopoulos D.Multilinear analysis of image ensembles:tensorfaces[J].European Conference on Computer Vision,2002(2350):447-460.
[13]Gene G,Charles V L.Matrix Computations[M].3rd edition.Baltimore:Johns Hopkins University Press,1996.
[14]Hao N,Kilmer M E,Braman K,et al.Facial recognition using tensor-tensor decompositions[J].Siam Journal on Imaging Sciences,2013,6(1):437-463.
[15]Kilmer M E,Braman K,Hao N,et al.Third order tensors as operators on matrices:a theoretical and computational framework with applications in imaging[J].Siam Journal on Matrix Analysis&Applications,2013,34(1):148-172.
[16]Braman K.Third-order tensors as linear operators on a space of matrices[J].Linear Algebra and Its Applications,2010,433(7):1241-1253.
[17]Zhang J,Saibaba A K,Kilmer M,et al.A randomized tensor singular value decomposition based on the t-product[J].Numerical Linear Algebra with Applications,2018,25(5):e2179.
[18]Bunch J R,Nielsen C P.Updating the singular value decomposition[J].Numerische Mathematik,1978,31(2):111-129.
[2]Karl Pearson.On lines and planes of cloest fit to systems of points in space[J].Philosophical Magazine,1901(2):559-572.
[3]马小龙.数据降维方法综述[D].北京:清华大学,2005.
[4]Yang J,Zhang D,Frangi A F,et al.Two-dimensional PCA:a new approach to appearance based face representation and recognition[J].IEEE Trans on Patten Analysis and Machine Intelligence,2004,26(1):131-137.
[5]Li M,Yuan B Z.2D-LDA:A statistical linear discriminant analysis for image matrix[J].Pattern Recognition Letters,2005,26(5):527-532.
[6]Yan S C,Xu D,Yang Q,et al.Multilinear discriminant analysis for face recognition[J].IEEE Trans on Image Processing,2007,16(1):212-220.
[7]Kolda T G,Bader B W.Tensor decompositions and applications[J].Siam Review,2009,51(3):455-500.
[8]Carroll J D,Chang J.Analysis of individual differences in multidimensional scaling via an n-way generalization of“eckart-young”decomposition[J].Psychometrika,1970,35(3):283-319.
[9]Tucker L R.Some mathematical notes on three-mode factor analysis[J].Psychometrika,1966,31(3):279-311.
[10]Lathauwer L D,Moor B D,Vandewalle J.A multilinear singular value decomposition[J].SIAM Journal of Matrix Analysis and Applications,2000,21(4):1253-1278.
[11]Kilmer M E,Martin C D.Factorization strategies for third-order tensors[J].Linear Algebra and Its Applications,2011,435(3):641-658.
[12]Vasilescu M A O,Terzopoulos D.Multilinear analysis of image ensembles:tensorfaces[J].European Conference on Computer Vision,2002(2350):447-460.
[13]Gene G,Charles V L.Matrix Computations[M].3rd edition.Baltimore:Johns Hopkins University Press,1996.
[14]Hao N,Kilmer M E,Braman K,et al.Facial recognition using tensor-tensor decompositions[J].Siam Journal on Imaging Sciences,2013,6(1):437-463.
[15]Kilmer M E,Braman K,Hao N,et al.Third order tensors as operators on matrices:a theoretical and computational framework with applications in imaging[J].Siam Journal on Matrix Analysis&Applications,2013,34(1):148-172.
[16]Braman K.Third-order tensors as linear operators on a space of matrices[J].Linear Algebra and Its Applications,2010,433(7):1241-1253.
[17]Zhang J,Saibaba A K,Kilmer M,et al.A randomized tensor singular value decomposition based on the t-product[J].Numerical Linear Algebra with Applications,2018,25(5):e2179.
[18]Bunch J R,Nielsen C P.Updating the singular value decomposition[J].Numerische Mathematik,1978,31(2):111-129.