Robust Joint Graph Learning for Multi-View Clustering

In real-world applications, multi-view datasets often comprise diverse data sources or views, inevitably accompanied by noise. However, most existing graph-based multi-view clustering methods utilize fixed graph similarity matrices to handle noisy multi-view data, necessitating additional clustering steps for obtaining the final clustering. This paper proposes a Robust Joint Graph learning for Multi-view Clustering (RJGMC) based on $ \ell _{1}$-norm to address these problems. RJGMC integrates the learning processes of the graph similarity matrix and the unified graph matrix to improve mutual reinforcement between these graph matrices. Simultaneously, employing the $ \ell _{1}$-norm to generate the unified graph matrix enhances the algorithm's robustness. A rank constraint is imposed on the graph Laplacian matrix of the unified graph matrix, where clustering can be divided directly without additional processing. In addition, we also introduce a method for automatically assigning optimal weights to each view. The optimization of this objective function employs an alternating optimization approach. Experimental results on synthetic and real-world datasets demonstrate that the proposed method outperforms other state-of-the-art techniques regarding clustering performance and robustness.