Abstract:

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.

Key words: face recognition, angle-based 2D Principal Component Analysis（angle-2DPCA）, Kernel-based 2D Principal Component Analysis（K2DPCA）, F-norm, Cholesky decompose

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。

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