基于低秩分解的鲁棒典型相关分析
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摘要
典型相关分析(CCA)是一种经典的多特征提取算法,它能够有效地抽取两组特征之间的相关性,现已被广泛应用于模式识别。在含噪声数据情况下,CCA的特征表示性能受到限制。为了使CCA更好地处理含噪声数据,提出一种基于低秩分解的典型相关分析算法——鲁棒典型相关分析(robust canonical correlation analysis,Rb CCA)。Rb CCA首先对特征集进行低秩分解,得到低秩分量和噪声分量,以此分别构建对应的协方差矩阵。通过最大化低秩分量的相关性,同时最小化噪声分量的相关性来建立判别准则函数,进而求取鉴别投影矢量。在MFEAT手写体数据库、ORL和Yale人脸数据中的实验结果表明,在包含噪声的情况下,Rb CCA的识别效果优于现有的典型相关分析方法。
Canonical correlation analysis( CCA) is a popular multi-feature extraction method,which can effectively explore the correlations between two sets of features. Up to now,CCA has been widely used in pattern recognition,however it has limited feature extraction power for large noisy data. For CCA to deal better with noisy data,a new method,robust canonical correlation analysis( Rb CCA),based on low rank decomposition,is proposed. Rb CCA first decomposes features using low rank decomposition to get the low rank and noisy components,then it constructs new covariance matrices based on these two components. A discriminative criteria function is further established to obtain discriminative projections by maximizing the correlations of the low rank component and minimizing the correlations of the noisy component. Experimental results on a MFEAT handwritten dataset,and ORL and Yale face datasets show that Rb CCA can achieve higher recognition rates than existing CCA methods,especially in noisy settings.
Canonical correlation analysis( CCA) is a popular multi-feature extraction method,which can effectively explore the correlations between two sets of features. Up to now,CCA has been widely used in pattern recognition,however it has limited feature extraction power for large noisy data. For CCA to deal better with noisy data,a new method,robust canonical correlation analysis( Rb CCA),based on low rank decomposition,is proposed. Rb CCA first decomposes features using low rank decomposition to get the low rank and noisy components,then it constructs new covariance matrices based on these two components. A discriminative criteria function is further established to obtain discriminative projections by maximizing the correlations of the low rank component and minimizing the correlations of the noisy component. Experimental results on a MFEAT handwritten dataset,and ORL and Yale face datasets show that Rb CCA can achieve higher recognition rates than existing CCA methods,especially in noisy settings.
引文
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[2]FISHER R A.The use of multiple measurements in axonomic problems[J].Annals of eugenics,1936,7(2):179-188.
[3]杨勇,蔡舒博.一种基于两步降维和并行特征融合的表情识别方法[J].重庆邮电大学学报:自然科学版,2015,27(3):377-387.YANG Yong,CAI Shubo.Facial expression recognition method based on two-steps dimensionality reduction and parallel feature fusion[J].Journal of chongqing university of posts and telecommunications:natural science edition,2015,27(3):377-387.
[4]HOU C,ZHANG C,WU Y,et al.Multiple view semisupervised dimensionality reduction[J].Pattern recognition,2010,43(3):720-730.
[5]HOTELLING H.Relations between two sets of variates[J].Biometrika,1936,28(3/4):321-377.
[6]孙权森,基于相关投影分析的特征抽取与图像识别研究[D].南京:南京理工大学,2006.SUN Quansen.Research on feature extraction and image recognition based on correlation projection analysis[D].Nanjing:Nanjing University of Science and Technology,2006.
[7]HOU Shudong,孙权森.稀疏保持典型相关分析及在特征融合中的应用[J].自动化学报,2012,38(4):659-665.HOU Shudong,SUN Quansen.Sparse maintaining canonical correlation analysis and its application in feature fusion[J].Journal of automation,2012,38(4):659-665.
[8]LIU G,LIN Z,YAN S,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.
[9]WRIGHT J,GANESH A,RAO S,et al.Robust principal component analysis:Exact recovery of corrupted low-rank matrices via convex optimization[C]//Advances in neural information processing systems.Vancouver,BC,Canada,2009:2080-2088.
[10]LIU G,LIN Z,YU Y.Robust subspace segmentation by low-rank representation[C]//Proceedings of the 27th international conference on machine learning(ICML-10).Haifa,Israel.2010:663-670.
[11]袁运浩.多重集典型相关分析理论及在高维多表示数据中的应用[D].南京:南京理工大学,2013.YUAN Yunhao.Canonical correlation analysis theory of multiple sets and its application in multi-representation data[D].Nanjing:Nanjing University of Science and Technology,2013.
[12]孙权森,曾生根,王平安,等.典型相关分析的理论及其在特征融合中的应用[J].计算机学报,2005,28(9):1524-1533.SUN Quansen,ZENG Shenggen,WANG Pingan,et al.The theory of canonical correlation analysis and its application in feature fusion[J].Chinese journal of computers,2005,28(9):1524-1533.
[13]张凡龙.基于核范数的低秩理论与方法研究[D].南京:南京理工大学,2015.ZHANG Fanlong.Research on low rank theory and method based on kernel norm[D].Nanjing:Nanjing University of Science and Technology,2015.
[14]CANDS E J,LI X,MA Y,et al.Robust principal component analysis[J].Journal of the ACM(JACM),2011,58(3):11.
[15]BAO B K,LIU G,XU C,et al.Inductive robust principal component analysis[J].IEEE transactions on image processing,2012,21(8):3794-3800.
[16]SHEN X B,SUN Q S,YUAN Y H.A unified multiset canonical correlation analysis framework based on graph embedding for multiple feature extraction[J].Neurocomputing,2015,148:397-408.
[17]FERDINANDO S,ANDY H.Parameterisation of a stochastic model for human face identification[C]//Proceedings of 2nd IEEE Workshop on Applications of Computer Vision.Sarasota FL,1994.
[18]BELHUMEUR P,HEPANHA J,KRIEGMAN D.Eigenfaces vs.Fisherfaces:recognition using class specific linear projection[J].IEEE transactions on pattern analysis and machine intelligence,1997,19(7):711-720.
[19]袁宝华,王欢,任明武.基于完整LBP特征的人脸识别[J].计算机应用研究,2012,29(4):1557-1559.YUAN Baohua,WANG Huan,REN Mingwu.Face recognition based on complete lbp feature[J].Journal of computer applications,2012,29(4):1557-1559.
[20]何国辉,甘俊英.二维主元分析在人脸识别中的应用研究[J].计算机工程与设计,2006,27(24):4667-4669.HE Guohui,GAN Junying.Application of two-dimensional principal component analysis in face recognition[J].Computer engineering and design,2006,27(24):4667-4669.
[21]赵军,赵艳,杨勇,等.基于降维的堆积降噪自动编码机的表情识别方法[J].重庆邮电大学学报:自然科学版,2016,28(6):844-848.ZHAO Jun,ZHAO Yan,YANG Yong,et al.Facial expression recognition method based on stacked denoisingauto-encoders and feature reduction[J].Journal of chongqing university of posts and telecommunications:natural science edition,2016,28(6):844-848.