Abstract: The color of facial images is one of the important features in face recognition, but the existing color face recognition based on 2D-PCA ignores its spatial relation. Therefore, a novel approach called Tensor PCA which uses a 3rd-order tensor to represent an RGB color image is proposed. In order to achieve the best classification, it seeks three projection matrices which consist of the eigenvectors corresponding to the largest eigenvalues of the n-mode total scatter matrix to maximize the distance of the projected samples, and constructs an ALS iterative procedure to optimize the projection matrices. As is shown in the results on Georgia Tech face database, in contrast with the process of 2D-PCA the recognition rate increases by 5.53% and the training time decreases by 78.1%.

Key words: face recognition, color information, two-Dimensional Principal Component Analysis（2D-PCA）, tensor

摘要： 人脸图像的色彩信息也是人脸的重要特征，但现有的2D-PCA彩色人脸识别忽略了人脸色彩信息的空间关系。由此引入三阶张量表示，提出基于张量的2D-PCA（Tensor PCA）的人脸识别算法。Tensor PCA通过分解[n]模总体散布矩阵获得三个由最大特征值对应的特征向量组成的将张量样本投影到低维子空间的投影矩阵，并构造交替最小二乘法的迭代过程对矩阵进行优化得到最优投影矩阵，使得投影后的样本间的距离尽可能得大，以达到最佳分类识别的效果。Georgia Tech彩色人脸库的测试结果表明，与2D-PCA方法相比，识别正确率提升了5.53%，同时训练时间降低了78.1%。

关键词: 人脸识别, 色彩信息, 二维主成分分析（2D-PCA）, 张量