基于张量的多线性思想对主成份分析方法的改进

张量的多线性方法把人脸图像看作是几何结构、表情、姿态和光照等多种因素的综合结果,运用张量方法分离出各个因素(如姿态,光照,人等)子空间,应用到人脸识别中。基于以上算法思想,提出主成份分析法(PCA)的一种改进方法,传统的PCA主要思想是将数据投影到正交的子空间中,改进后的PCA主要思想是:先对图像降维以减少图像矩阵的维数,然后,通过分解三维颜色张量的方法加入颜色信息,对张量进行中心化,运用张量方法进行人脸识别。实验结果表明该算法能有效提高性能。

An Improvement of PCA Based on the Idea of Multi-linear of Tensor

Tensor-based multilinear approaches regard human face as the composite consequence of geometries,viewpoints and illuminations,and use tensor decomposing algebra to get factor(i.e viewpoint,illumination,person,etc) subspaces for recognition.Based on the above idea,we proposed an improvement of PCA: traditional PCA performs SVD decomposition on face image data: A= U∑VT and recognizes human face by projecting to U,now we project to U∑,the idea is that V represents the sample space,so we project the unknown face to U∑ and compare it to V,then we can find the nearest point in the sample space V,which the unknown belongs to.Here we give a few experiments and the results show the method performs better.