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Multi-view clustering (MVC) aims at exploring category structures among multi-view data in self-supervised manners. Multiple views provide more information than single views and thus existing MVC methods can achieve satisfactory performance. However their performance might seriously degenerate when the views are noisy in practical multi-view scenarios. In this paper we formally investigate the drawback of noisy views and then propose a theoretically grounded deep MVC method (namely MVCAN) to address this issue. Specifically we propose a novel MVC objective that enables un-shared parameters and inconsistent clustering predictions across multiple views to reduce the side effects of noisy views. Furthermore a two-level multi-view iterative optimization is designed to generate robust learning targets for refining individual views' representation learning. Theoretical analysis reveals that MVCAN works by achieving the multi-view consistency complementarity and noise robustness. Finally experiments on extensive public datasets demonstrate that MVCAN outperforms state-of-the-art methods and is robust against the existence of noisy views.