中文摘要：

人脸识别中,传统数据降维方法将人脸图像重排列成向量后进行处理,丢失了数据本身的结构特性,导致识别精度不高。本文发展了一种基于张量的数据降维方法——多维正交判别子空间投影。该算法直接用张量描述人脸,并通过张量到矢量投影（tensor to vector projection,TVP）将张量数据投影到向量判别子空间。此方法寻找相互正交的投影向量集,使得判别子空间中数据类间离散度最大,同时类内离散度最小;进而利用TVP投影将高维张量数据映射成低维向量数据,在合适的约束条件下,这些降维后的向量特征数据是整个人脸数据中最具代表性的特征数据;最后,使用k最近邻（KNN）分类器将这些特征数据分类。利用经典人脸数据库ORL进行实验,验证了本文方法的有效性。

英文摘要：

Traditional dimensionality reduction methods in face recognition are methods that reshape tensor face into a vector, which may lose the structural characteristics of the original data, leading to a relatively low identification result. We present a dimensionality reduction method multilinear discriminant subspace projection （MDSP） based on tensor. Our algorithm aims to use tensor to de- scribe face data directly, and project the tensor data onto the vector discriminant subspace through a new kind of projection method tensor to vector projection （TVP）. To reach this target, the algo- rithm first finds out the projection vectors （PV） that make data in the discriminant subspace get the maximum between-class scatter as well as the minimum within-class scatter. Then with the help of PV, tensor data can be projected into the low dimensional vector data. As long as proper constraints are given, the vector data can be the most representative feature data. The feature data is then sent to the KNN classifier for classification. Results in experiments on databases ORL confirm the veracity of our algorithm.