中文摘要：

经典的向量子空间学习算法是以数据流形的向量表示进行计算的,但是在现实世界中数据流形从本质上而言是以张量的形式存在,因此基于张量子空间的学习算法能够更好地揭示流形内在的几何结构.本文提出了一种新的张量子空间的学习算法：张量局部判别投影.首先构建类内和类间图,然后保持流形的局部结构并且利用数据的判别信息,推导出算法的计算公式,最后通过迭代计算广义特征向量,解得最优张量子空间.在标准人脸数据库上的实验表明该算法有效.

英文摘要：

Classical vector subspace learning algorithms work with vectorized representations of data manifold, while data manifold represented in the reality is intrinsically a tensor, so the algorithms based on tensor subspace leamig can perfectly detect the intrinsic geometrical structure of the data manifold. In this paper, a novel tensor subspace learning algorithm, tensor locality discriminant projection, is proposed. To implement the algorithm, construct within-class and between-class graph at first, then preserve local structure of the data manifold and utilize its discriminant information to deduce the formula of the algorithm, finally work out optimal tensor subspace by iteratively computing the generalized eigenvectors. The experiments on the standard face database demonstrate the effectiveness of the proposed algorithm.