张量典型相关分析及其在人脸识别中的应用

摘要

In the real world many data sources exist in the form of tensor, so the learning algorithm based on tensor space can describe the semantic information of data sources better. This paper presents a new tensor correlation analysis algorithm, with which we can directly analyze the tensor data. Because of the large reduction of the dimension of eigenvalue decomposition covariance matrix, the algorithm can effectively reduce the computing complexity and avoid the covariance matrix singular problem. The effectiveness of this method can be proved at YALE, ORL face database.%针对源数据向量化常导致很高的数据维数,易使向量型学习算法陷入雏数灾难和样本个数远小于特征维数的小样本问题,提出了一种新的张量典型相关分析算法,能直接对张量数据进行典型相关分析,由于其特征值分解的协方差矩阵雏数大幅度减少,能有效降低计算复杂度和协方差矩阵奇异的问题.在Yale、ORL脸数据库上验证了本文方法的有效性.