A splitting method for the locality regularized semi-supervised subspace clustering

Graph-based semi-supervised learning (G-SSL) methods play an increasingly important role in machine learning systems. Recently, latent low-rank representation (LatLRR) graph has gained great success in subspace clustering. However, LatLRR only considers the global structure, while the local geometric information, which is often important to many real applications, is ignored. In this paper, we propose a locality regularized LatLRR model (LR-LatLRR) for semi-supervised subspace clustering problems. This model incorporates two regularization terms into LatLRR by taking the local structure of data into account. Then, we develop an efficient splitting algorithm for solving LR-LatLRR. In addition, we also prove the global convergence of the proposed algorithm. Furthermore, we extend the LR-LatLRR model to a case of including the non-negative constraint. Finally, we conduct experiments on a synthetic data and several real data sets for the semi-supervised clustering problems. Experimental results show that our method can obtain high classification accuracy and outperforms several state-of-the-art G-SSL methods.