非线性角度2DPCA及其在人脸识别中的应用  

Nolinear Angle 2DPCA and Its Application on Face Recognition

作　　者：乔慧 周水生 QIAO Hui;ZHOU Shuisheng(School of Mathematics and Statistics,Xidian University,Xi’an 710126,China)

机构地区：[1]西安电子科技大学数学与统计学院,西安710126

出　　处：《计算机工程与应用》2021年第8期112-118,共7页Computer Engineering and Applications

基　　金：国家自然科学基金(61772020)。

摘　　要：K2DPCA(Kernel-based 2D Principal Component Analysis)能够刻画图像的非线性特征,同时保留原始图像的二维数据结构和邻域信息,在人脸识别领域具有成功的运用,但其对异常值比较敏感。为克服此问题,将“角度”的概念引入非线性空间,基于核方法提出Sin-K2DPCA,并采用F范数度量,将样本数据经非线性映射到高维空间后极小化相对重构误差。为进一步解决非线性的核矩阵规模较大、计算复杂度高的问题,利用Cholesky分解方法,计算大规模核矩阵K的低秩近似,提出了基于Cholesky分解的Chol+SinK2DPCA。实验结果表明,在ORL、Yale人脸数据库中,Chol+SinK2DPCA提高了识别率,并克服噪声的影响;在大规模数据集Extended YaleB中,Chol+SinK2DPCA有效解决了K2DPCA由于核矩阵规模过大而不能实现的问题。K2DPCA(Kernel-based 2D Principal Component Analysis)can depict the nonlinear features of the image,preserving the two-dimensional data structure and neighborhood information of the original image,which has been successfully applied in the field of face recognition.However,it is sensitive to outliers.To overcome this problem,Sin-K2DPCA method based on the kernel is proposed by introducing the concept of angle into the nonlinear space and using the F-norm measure to minimize the relative reconstruction error after mapping the sample data nonlinearly to the high-dimensional space.Further more,to solve the problem of large size and high computational complexity of nonlinear kernel matrix K,Chol+SinK2DPCA method based on the Cholesky decomposition is proposed by using the Cholesky decomposition method to calculate the low-rank approximation of the large-scale nuclear matrix.The experimental results show that Chol+SinK2DPCA improves the recognition rate and overcomes the influence of noise in the ORL,YALE face database.Simultaneously,in the large-scale dataset Extended YaleB,Chol+SinK2DPCA effectively solves the problem that K2DPCA cannot be realized because of the large size of the kernel matrix.

关 键 词：人脸识别 角度二维主成分分析(angle-2DPCA) 基于核的二维主成分分析(K2DPCA) F范数 CHOLESKY分解 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]