中文说明：应用背景几何结构分析是进行数据处理的重要基础，已经被广泛应用在人脸识别、手写体数字识别、图像分类、等模式识别和数据分类问题，以及图象分割、运动分割等计算机视觉问题（人脸识别、图像分类、运动分割等实例见下文）中。关键技术通过对子空间表示系数矩阵的研究，有些学者在求解子空间表示系数矩阵时，引入核范数（一个矩阵的核范数是指矩阵的所有奇异值的加和）约束，希望通过系数矩阵的低秩要求得到更好的数据的子空间表示。文章[ 4 ]给出了低秩表示模型的闭解且理论上保证了当子空间独立且数据采样充分的情况时，低秩表示可以得到块对角的解这个结论基本保证了低秩表示方法在解决独立子空间分割问题的有效性。
English Description：
Background geometric structure analysis is an important basis for data processing. It has been widely used in face recognition, handwritten numeral recognition, image classification, pattern recognition and data classification, as well as image segmentation, motion segmentation and other computer vision problems (examples of face recognition, image classification and motion segmentation are shown below). Key technology through the study of subspace representation coefficient matrix, some scholars introduce the kernel norm (the kernel norm of a matrix refers to the sum of all singular values of the matrix) constraint when solving the subspace representation coefficient matrix, hoping to get a better subspace representation of data through the low rank requirement of the coefficient matrix. The paper [4] gives the closed solution of the low rank representation model, and theoretically guarantees that when the subspace is independent and the data sampling is sufficient, the low rank representation can get the block diagonal solution. This conclusion basically guarantees the effectiveness of the low rank representation method in solving the independent subspace segmentation problem.