The multi-view subspace clustering attracts much attention in recent years. Most methods follow the framework of fusing the affinity graph learned in each view. In this framework, both the fusion strategy and built graph of each view are very important. In this paper, we propose novel methods for multi-view subspace clustering to address these two aspects. On the one hand, we adopt the autoencoders with Laplacian regularization to construct the affinity graph in each view. Compared with previous work employing the autoencoders, the Laplacian term in our method can guide the learned latent representation favoring affinity extraction. Besides, we also discuss the reasons for adding Laplacian regularization. On the other hand, we propose a novel fusion strategy distinguished from the related literature. If the affinity graph of some view is not extracted well, the performance of previous fusion strategies will be seriously affected. Since our strategy can choose the best part from each affinity graph, it can overcome this limitation to some extent. Extensive experimental results on multiple benchmark data sets confirm the effectiveness of our method.

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.