中文摘要：

传统的图像数据（n1×n2）一般表示为欧式空间R（n1×n2）上的一个向量，这样像素之间的空间关系将会丢失．因此，文中提出一种张量型的半监督降维算法．首先把图像看成张量空间Rn1×Rn2。中的一个点．再利用图像之间的成对约束——正约束和负约束，对图像进行半监督降维．降维后的数据较好地保留图像的局部结构．在大量人脸数据集上的实验验证该算法的有效性．

英文摘要：

Traditionally, an （n1 ＊ n2 ） image is represented by a vector in the Euclidean space R（n1 ＊ n2） , thus the spatial relationships between pixels in an image are ignored. In this paper, the images are presented as points in the tensor space Rn1 × Rn2 . Then, a semi-supervised dimensionality reduction algorithm is put forward based on pairwise constraints （must-link and cannot-link）between the images. The data in the reduced space preserve the local structure of the data manifold well. Finally, experimental results on face datasets validate the effectiveness of the proposed algorithm.