Low-rank representation (LRR) and its variants have been proved to be powerful tools for handling subspace clustering problems. Most of these methods involve a sub-problem of computing the singular value decomposition of an matrix, which leads to a computation complexity of . Obviously, when n is large, it will be time consuming. To address this problem, the authors introduce a fast solution, which reformulates the large-scale problem to an equal form with smaller size. Thus, the proposed method remarkably reduces the computation complexity by solving a small-scale problem. Theoretical analysis proves the efficiency of the proposed model. Furthermore, we extend LRR to a general model by using Schatten p -norm instead of nuclear norm and present a fast algorithm to solve large-scale problem. Experiments on MNIST and Caltech101 databse illustrate the equivalence of the proposed algorithm and the original LRR solver. Experimental results show that the proposed algorithm is remarkably faster than traditional LRR algorithm, especially in the case of large sample number.

中文翻译：

---

LRR的大规模子空间聚类快速算法

低秩表示（LRR）及其变体已被证明是处理子空间聚类问题的强大工具。这些方法中的大多数涉及一个子问题，该子问题用于计算 矩阵，导致计算复杂度为 。显然，当ñ很大，会很费时间。为了解决这个问题，作者介绍了一种快速解决方案，该解决方案将大规模问题重新构造为大小较小的相等形式。因此，所提出的方法通过解决小规模问题而显着降低了计算复杂度。理论分析证明了该模型的有效性。此外，我们通过使用Schatten将LRR扩展到通用模型p -范数而不是核范数，并提出了一种解决大规模问题的快速算法。在MNIST和Caltech101数据库上进行的实验说明了该算法与原始LRR求解器的等效性。实验结果表明，该算法比传统的LRR算法有明显的提高，特别是在样本数较大的情况下。