结构化加权稀疏低秩恢复算法在人脸识别中的应用
|
摘要
针对训练样本或测试样本存在污损的情况,提出一种结构化加权稀疏低秩恢复算法(structured and weighted-sparse low rank representation,SWLRR)。SWLRR对低秩表示进行加权稀疏约束和结构化约束,使得低秩表示系数更加趋近于块对角结构,进而可获得具有判别性的低秩表示。SWLRR将训练样本恢复成干净训练样本后,再根据原始训练样本和恢复后的训练样本学习到低秩投影矩阵,把测试样本投影到相应的低秩子空间,即可有效地去除测试样本中的污损部分。在几个人脸数据库上的实验结果验证了SWLRR在不同情况下的有效性和鲁棒性。
Herein, a structured and weighted sparse low-rank recovery algorithm(SWLRR) is proposed to deal with trained or tested samples that are corrupt. The SWLRR constrains the low-rank representation by incorporating the structured and weighted sparse constraints, enabling the low-rank representation coefficient matrix to be closer to the block diagonal. Then, a discriminative structured representation can be obtained. After recovering the clean training samples from the corrupted training samples using SWLRR, the low-rank projection matrix is learnt by the low-rank projection matrix according to the original and recovered training samples, whereas the test samples are projected into the corresponding low-rank subspaces. In this way, the corrupted regions can be removed efficiently from the test samples. The experimental results on several face databases validate the effectiveness and robustness of the SWLRR under different situations.
Herein, a structured and weighted sparse low-rank recovery algorithm(SWLRR) is proposed to deal with trained or tested samples that are corrupt. The SWLRR constrains the low-rank representation by incorporating the structured and weighted sparse constraints, enabling the low-rank representation coefficient matrix to be closer to the block diagonal. Then, a discriminative structured representation can be obtained. After recovering the clean training samples from the corrupted training samples using SWLRR, the low-rank projection matrix is learnt by the low-rank projection matrix according to the original and recovered training samples, whereas the test samples are projected into the corresponding low-rank subspaces. In this way, the corrupted regions can be removed efficiently from the test samples. The experimental results on several face databases validate the effectiveness and robustness of the SWLRR under different situations.
引文
[1]TURK M,PENTLAND A.Eigenfaces for recognition[J].Journal of cognitive neuroscience,1991,3(1):71-86.
[2]BELHUMEUR P N,HESPANHA J P,KRIEGMAN D J.Eigenfaces vs.fisherfaces:recognition using class specific linear projection[J].IEEE transactions on pattern analysis and machine intelligence,997,19(7):711-720.
[3]LIU Chengjun,WECHSLER H.Gabor feature based classification using the enhanced fisher linear discriminant model for face recognition[J].IEEE transactions on image processing,2002,11(4):467-476.
[4]HE Xiaofei,YAN Shuicheng,HU Yuxiao,et al.Face recognition using Laplacianfaces[J].IEEE transactions on pattern analysis and machine intelligence,2005,27(3):328-340.
[5]WRIGHT J,YANG A Y,GANESH A,et al.Robust face recognition via sparse representation[J].IEEE transactions on pattern analysis and machine intelligence,2009,31(2):210-227.
[6]MIN R,DUGELAY J L.Improved combination of LBPand sparse representation based classification(SRC)for face recognition[C]//Proceedings of 2011 IEEE ICME.Barcelona,Spain,2011:1-6.
[7]CHEN C F,WEI C P,WANG Y C F.Low-rank matrix recovery with structural incoherence for robust face recognition[C]//Proceedings of 2012 IEEE Conference on Computer Vision and Pattern Recognition.Providence,USA,2012:2618-2625.
[8]YANG Meng,ZHANG Lei,YANG Jian,et al.Regularized robust coding for face recognition[J].IEEE transactions on image processing,2013,22(5):1753-1766.
[9]ZHANG Lei,YANG Meng,FENG Xiangchu.Sparse representation or collaborative representation:which helps face recognition?[C]//Proceedings of 2011 ICCV.Barcelona,Spain,2011:471-478.
[10]DENG Weihong,HU Jiani,GUO Jun.Extended SRC:undersampled face recognition via intraclass variant dictionary[J].IEEE transactions on pattern analysis and machine intelligence,2012,34(9):1864-1870.
[11]YANG Meng,ZHU Pengfei,LIU Feng,et al.Joint representation and pattern learning for robust face recognition[J].Neurocomputing,2015,168:70-80.
[12]CANDèS E J,LI Xiaodong,MA Yi,et al.Robust principal component analysis[J].Journal of the ACM,2011,58(3):11.
[13]LIU Guangcan,LIN Zhouchen,YAN Shuicheng,et al.Robust recovery of subspace structures by low-rank representation[J].IEEE transactions on pattern analysis and machine intelligence,2013,35(1):171-184.
[14]MA Long,WANG Chunheng,XIAO Baihua,et al.Sparse representation for face recognition based on discriminative low-rank dictionary learning[C]//Proceedings of 2012IEEE Conference on Computer Vision and Pattern Recognition.Providence,USA,2012:2586-2593.
[15]ZHANG Yangmuzi,JIANG Zhuolin,DAVIS L S.Learning structured low-rank representations for image classification[C]//Proceeding of 2013 IEEE Conference on Computer Vision and Pattern Recognition.Portland,USA,2013:676-683.
[16]NGUYEN H,YANG Wankou,SHENG Biyun,et al.Discriminative low-rank dictionary learning for face recognition[J].Neurocomputing,2016,173(3):541-551.
[17]CHANG Heyou,ZHENG Hao.Weighted discriminative dictionary learning based on lowrank representation[J].Journal of physics:conference series,2017,90:012009.
[18]ZHANG Zheng,XU Yong,SHAO Ling,et al.Discriminative block-diagonal representation learning for image recognition[J].IEEE transactions on neural networks and learning systems,2018,29(7):3111-3125.
[19]CHEN Jie,YI Zhang.Sparse representation for face recognition by discriminative low-rank matrix recovery[J].Journal of visual communication and image representation,2014,25(5):763-773.
[20]COSTEIRA J P,KANADE T.A multibody factorization method for independently moving objects[J].International journal of computer vision,1998,29(3):159-179.
[21]ZHUANG Liansheng,GAO Haoyuan,LIN Zhouchen,et al.Non-negative low rank and sparse graph for semi-supervised learning[C]//Proceedings of 2012 IEEE Conference on Computer Vision and Pattern Recognition.Providence,USA,2012:2328-2335.
[22]LIN Zhouchen,LIU Risheng,SU Zhixun.Linearized alternating direction method with adaptive penalty for lowrank representation[J].Advance in neural information processing systems,2011:612-620.
[23]LIN Zhouchen,CHEN Minming,MA Yi.The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices[R].Urbana-Champaign:University of Illinois at Urbana-Champaign,2009.
[24]BAO Bingkun,LIU Guangcan,XU Changsheng,et al.Inductive robust principal component analysis[J].IEEEtransactions on image processing,2012,21(8):3794-3800.
[25]CORTES C,VAPNIK V.Support-vector networks[J].Machine learning,1995,20(3):273-297.
[26]HEISELE B,HO P,POGGIO T.Face recognition with support vector machine:global versus component-based approach[C]//Proceedings Eighth IEEE International Conference on Computer Vision.Vancouver,BC,Canada,2001:688-694.
[27]CHANG C C,LIN C J.Libsvm:a library for support vector machines[J].ACM transactions on intelligent systems and technology,2011,2(3):1-27.
[28]MARTINEZ A,BENAVENTE R.The AR face database[R].CVC Technical Report No.24.Barcelona:Universitat Autonoma de Barcelona,1998.
[29]GEORGHIADES A S,BELHUMEUR P N,KRIEG-MAN D J.From few to many:illumination cone models for face recognition under variable lighting and pose[J].IEEE transactions on pattern analysis and machine intelligence,2001,23(6):643-660.
[30]LEE K C,HO J,KRIEGMAN D J.Acquiring linear subspaces for face recognition under variable lighting[J].IEEE transactions on pattern analysis and machine intelligence,2005,27(5):684-698.
[31]SIM T,BAKER S,BSAT M.The CMU pose,illumination,and expression database[J].IEEE transactions on pattern analysis and machine intelligence,2003,25(12):1615-1618.
[2]BELHUMEUR P N,HESPANHA J P,KRIEGMAN D J.Eigenfaces vs.fisherfaces:recognition using class specific linear projection[J].IEEE transactions on pattern analysis and machine intelligence,997,19(7):711-720.
[3]LIU Chengjun,WECHSLER H.Gabor feature based classification using the enhanced fisher linear discriminant model for face recognition[J].IEEE transactions on image processing,2002,11(4):467-476.
[4]HE Xiaofei,YAN Shuicheng,HU Yuxiao,et al.Face recognition using Laplacianfaces[J].IEEE transactions on pattern analysis and machine intelligence,2005,27(3):328-340.
[5]WRIGHT J,YANG A Y,GANESH A,et al.Robust face recognition via sparse representation[J].IEEE transactions on pattern analysis and machine intelligence,2009,31(2):210-227.
[6]MIN R,DUGELAY J L.Improved combination of LBPand sparse representation based classification(SRC)for face recognition[C]//Proceedings of 2011 IEEE ICME.Barcelona,Spain,2011:1-6.
[7]CHEN C F,WEI C P,WANG Y C F.Low-rank matrix recovery with structural incoherence for robust face recognition[C]//Proceedings of 2012 IEEE Conference on Computer Vision and Pattern Recognition.Providence,USA,2012:2618-2625.
[8]YANG Meng,ZHANG Lei,YANG Jian,et al.Regularized robust coding for face recognition[J].IEEE transactions on image processing,2013,22(5):1753-1766.
[9]ZHANG Lei,YANG Meng,FENG Xiangchu.Sparse representation or collaborative representation:which helps face recognition?[C]//Proceedings of 2011 ICCV.Barcelona,Spain,2011:471-478.
[10]DENG Weihong,HU Jiani,GUO Jun.Extended SRC:undersampled face recognition via intraclass variant dictionary[J].IEEE transactions on pattern analysis and machine intelligence,2012,34(9):1864-1870.
[11]YANG Meng,ZHU Pengfei,LIU Feng,et al.Joint representation and pattern learning for robust face recognition[J].Neurocomputing,2015,168:70-80.
[12]CANDèS E J,LI Xiaodong,MA Yi,et al.Robust principal component analysis[J].Journal of the ACM,2011,58(3):11.
[13]LIU Guangcan,LIN Zhouchen,YAN Shuicheng,et al.Robust recovery of subspace structures by low-rank representation[J].IEEE transactions on pattern analysis and machine intelligence,2013,35(1):171-184.
[14]MA Long,WANG Chunheng,XIAO Baihua,et al.Sparse representation for face recognition based on discriminative low-rank dictionary learning[C]//Proceedings of 2012IEEE Conference on Computer Vision and Pattern Recognition.Providence,USA,2012:2586-2593.
[15]ZHANG Yangmuzi,JIANG Zhuolin,DAVIS L S.Learning structured low-rank representations for image classification[C]//Proceeding of 2013 IEEE Conference on Computer Vision and Pattern Recognition.Portland,USA,2013:676-683.
[16]NGUYEN H,YANG Wankou,SHENG Biyun,et al.Discriminative low-rank dictionary learning for face recognition[J].Neurocomputing,2016,173(3):541-551.
[17]CHANG Heyou,ZHENG Hao.Weighted discriminative dictionary learning based on lowrank representation[J].Journal of physics:conference series,2017,90:012009.
[18]ZHANG Zheng,XU Yong,SHAO Ling,et al.Discriminative block-diagonal representation learning for image recognition[J].IEEE transactions on neural networks and learning systems,2018,29(7):3111-3125.
[19]CHEN Jie,YI Zhang.Sparse representation for face recognition by discriminative low-rank matrix recovery[J].Journal of visual communication and image representation,2014,25(5):763-773.
[20]COSTEIRA J P,KANADE T.A multibody factorization method for independently moving objects[J].International journal of computer vision,1998,29(3):159-179.
[21]ZHUANG Liansheng,GAO Haoyuan,LIN Zhouchen,et al.Non-negative low rank and sparse graph for semi-supervised learning[C]//Proceedings of 2012 IEEE Conference on Computer Vision and Pattern Recognition.Providence,USA,2012:2328-2335.
[22]LIN Zhouchen,LIU Risheng,SU Zhixun.Linearized alternating direction method with adaptive penalty for lowrank representation[J].Advance in neural information processing systems,2011:612-620.
[23]LIN Zhouchen,CHEN Minming,MA Yi.The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices[R].Urbana-Champaign:University of Illinois at Urbana-Champaign,2009.
[24]BAO Bingkun,LIU Guangcan,XU Changsheng,et al.Inductive robust principal component analysis[J].IEEEtransactions on image processing,2012,21(8):3794-3800.
[25]CORTES C,VAPNIK V.Support-vector networks[J].Machine learning,1995,20(3):273-297.
[26]HEISELE B,HO P,POGGIO T.Face recognition with support vector machine:global versus component-based approach[C]//Proceedings Eighth IEEE International Conference on Computer Vision.Vancouver,BC,Canada,2001:688-694.
[27]CHANG C C,LIN C J.Libsvm:a library for support vector machines[J].ACM transactions on intelligent systems and technology,2011,2(3):1-27.
[28]MARTINEZ A,BENAVENTE R.The AR face database[R].CVC Technical Report No.24.Barcelona:Universitat Autonoma de Barcelona,1998.
[29]GEORGHIADES A S,BELHUMEUR P N,KRIEG-MAN D J.From few to many:illumination cone models for face recognition under variable lighting and pose[J].IEEE transactions on pattern analysis and machine intelligence,2001,23(6):643-660.
[30]LEE K C,HO J,KRIEGMAN D J.Acquiring linear subspaces for face recognition under variable lighting[J].IEEE transactions on pattern analysis and machine intelligence,2005,27(5):684-698.
[31]SIM T,BAKER S,BSAT M.The CMU pose,illumination,and expression database[J].IEEE transactions on pattern analysis and machine intelligence,2003,25(12):1615-1618.