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

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