Grassmann流形上的低秩表示：一个外化的观点
Low Rank Representation on Grassmann Manifolds: An Extrinsic Perspective
摘要：
许多计算机视觉算法采用子空间模型来表示数据。低秩表示（LRR）已成功地应用于子空间聚类，数据根据其子空间结构进行聚类。本文探讨了在Grassmann流形上推广LRR的可能性。不是直接将格拉斯曼流形嵌入到对称矩阵空间中，而是通过在每个格拉斯曼点的切空间上构建LRR的自表示来采取外在观点。设计并实现了一种新的算法来求解所提出的格拉斯曼LRR模型。在手写数字数据集、动态纹理视频片段和YouTube名人人脸视频数据上进行了聚类实验。实验结果表明，我们的方法优于一些现有的方法。
英文摘要：
Many computer vision algorithms employ subspace models to represent data. The Low-rank representation (LRR) has been successfully applied in subspace clustering for which data are clustered according to their subspace structures. The possibility of extending LRR on Grassmann manifold is explored in this paper. Rather than directly embedding Grassmann manifold into a symmetric matrix space, an extrinsic view is taken by building the self-representation of LRR over the tangent space of each Grassmannian point. A new algorithm for solving the proposed Grassmannian LRR model is designed and implemented. Several clustering experiments are conducted on handwritten digits dataset, dynamic texture video clips and YouTube celebrity face video data. The experimental results show our method outperforms a number of existing methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
