Multi-view subspace clustering with adaptive locally consistent graph regularization

Graph regularization has shown its effectiveness in multi-view subspace clustering methods. Many multi-view subspace clustering methods based on graph regularization build the adjacency matrix directly based on a simple similarity measure between data points for each view. However, these simply constructed graphs are sensitive to light corruptions and even generate misleading manifold. Considering this shortcoming, this paper presents a multi-view subspace clustering algorithm (CGMSC) with a well-defined locally consistent graph regularization. We formulate CGMSC by a two-stage procedure. In the first stage, an adaptive self-weighted multi-view local linear embedding (ASWMVLLE) method is proposed to build the locally consistent geometric relationship between instances. In the second stage, ASWMVLLE is introduced into CGMSC by defining a local graph regularization term about the consensus latent subspace representation, which can not only effectively keep the manifold structure of data, but also ensure the consistency across different views. Experiments on eight real-world datasets demonstrate that our method has good robustness and clustering performance.