Robust Principal Component Analysis with Projection Learning for Image Classification

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.