Structure-Constrained Low-Rank Representation

Benefiting from its effectiveness in subspace segmentation, low-rank representation (LRR) and its variations have many applications in computer vision and pattern recognition, such as motion segmentation, image segmentation, saliency detection, and semisupervised learning. It is known that the standard LRR can only work well under the assumption that all the subspaces are independent. However, this assumption cannot be guaranteed in real-world problems. This paper addresses this problem and provides an extension of LRR, named structure-constrained LRR (SC-LRR), to analyze the structure of multiple disjoint subspaces, which is more general for real vision data. We prove that the relationship of multiple linear disjoint subspaces can be exactly revealed by SC-LRR, with a predefined weight matrix. As a nontrivial byproduct, we also illustrate that SC-LRR can be applied for semisupervised learning. The experimental results on different types of vision problems demonstrate the effectiveness of our proposed method.