PDRLRR: A novel low-rank representation with projection distance regularization via manifold optimization for clustering

The low-rank representation (LRR) method has attracted widespread attention due to its excellent performance in pattern recognition and machine learning. LRR-based variants have been proposed to solve the three existing problems in LRR: (1) the projection matrix is permanently fixed when dimensionality reduction techniques are adopted; (2) LRR fails to capture the local geometric structure; and (3) the solution deviates from the real low-rank solution. To address these problems, this paper proposes a low-rank representation with projection distance regularization (PDRLRR) via manifold optimization for clustering. In detail, we first introduce a low-dimensional projection matrix and a projection distance regularization term to fit the projected data automatically and capture the local structure of the data, respectively. Consequently, the projection matrix and representation matrix are obtained jointly. Then, we obtain a more accurate low-rank solution by minimizing the Schatten-p norm instead of the nuclear norm. Next, the projection matrix is optimized through a generalized Stiefel manifold. Extensive experiments demonstrate that our proposed method outperforms the state-of-the-art methods. •This paper proposes a novel PDRLRR model that can simultaneously address the three common problems in LRR.•Data dimensionality reduction technology is integrated into LRR, reducing the data dimensions while learning representation matrices.•For extracting the complete information, the projection distance regularization term is introduced to capture the global and local structure of the data.•The Schatten-p norm instead of the nuclear norm is employed to solve the rank minimization problem of the representation matrix, which can more accurately approximate the real low-rank solution.