关键词: 张量, 充分降维, 迭代算法, 图像识别

Abstract: In the era of big data, a large amount of tensor data are generated in many fields such as finance, genomics and image processing. Zhong et al. (2015) propose tensor sufficient dimension reduction and present a sequential iterative algorithm for second-order tensors. In view of the wide application of highorder tensors in real life, this paper extends the iterative algorithm of Zhong et al. (2015) to higher-order tensors. Taking third-order tensors as an example, two different algorithms are proposed: structural transformation algorithm and structural maintenance algorithm. The two algorithms can effectively reduce the variable dimension and computational complexity while maintaining the original structural information of tensors, avoiding the singular problem of covariance matrix. The two algorithms are applied to the classification and recognition of color facial images. Then 2-D and 3-D scatter plots are used to display the classification results of the algorithms. Comparing the structural maintenance algorithm with the K-means clustering method, t-SNE nonlinear dimension reduction method, multilinear principal component analysis, multilinear discriminant analysis and tensor SIR, the paper shows that the proposed method has obvious advantages in classification accuracy, and has broad development prospect in image recognition and related fields of application.

Key words: Tensor, Sufficient Dimension Reduction, Iterative Algorithm, Image Recognition