ABSTRACT In this paper, we propose a robust subspace learning method, based on RPCA, named Robust Principal Component Analysis with Projection Learning (RPCAPL), which further improves the performance of feature extraction by projecting data samples into a suitable subspace. For Subspace Learning (SL) methods in clustering and classification tasks, it is also critical to construct an appropriate graph for discovering the intrinsic structure of the data. For this reason, we add a graph Laplacian matrix to the RPCAPL model for preserving the local geometric relationships between data samples and name the improved model as RPCAGPL, which takes all samples as nodes in the graph and treats affinity between pairs of connected samples as weighted edges. The RPCAGPL can not only globally capture the low-rank subspace structure of the data in the original space, but also locally preserve the neighbor relationship between the data samples.

中文翻译：

---

用于图像分类的具有投影学习的稳健主成分分析

摘要 在本文中，我们提出了一种基于 RPCA 的鲁棒子空间学习方法，称为带有投影学习的鲁棒主成分分析（RPCAPL），通过将数据样本投影到合适的子空间，进一步提高了特征提取的性能。对于聚类和分类任务中的子空间学习 (SL) 方法，构建适当的图以发现数据的内在结构也很重要。为此，我们在 RPCAPL 模型中添加了一个图拉普拉斯矩阵以保留数据样本之间的局部几何关系，并将改进的模型命名为 RPCAGPL，它将所有样本作为图中的节点，并将连接样本对之间的亲和度视为加权边缘。