Robust auto-weighted multi-view subspace clustering with common subspace representation matrix

In many computer vision and machine learning applications, the data sets distribute on certain low-dimensional subspaces. Subspace clustering is a powerful technology to find the underlying subspaces and cluster data points correctly. However, traditional subspace clustering methods can only be applied on data from one source, and how to extend these methods and enable the extensions to combine information from various data sources has become a hot area of research. Previous multi-view subspace methods aim to learn multiple subspace representation matrices simultaneously and these learning task for different views are treated equally. After obtaining representation matrices, they stack up the learned representation matrices as the common underlying subspace structure. However, for many problems, the importance of sources and the importance of features in one source both can be varied, which makes the previous approaches ineffective. In this paper, we propose a novel method called Robust Auto-weighted Multi-view Subspace Clustering (RAMSC). In our method, the weight for both the sources and features can be learned automatically via utilizing a novel trick and introducing a sparse norm. More importantly, the objective of our method is a common representation matrix which directly reflects the common underlying subspace structure. A new efficient algorithm is derived to solve the formulated objective with rigorous theoretical proof on its convergency. Extensive experimental results on five benchmark multi-view datasets well demonstrate that the proposed method consistently outperforms the state-of-the-art methods.