Abstract: As it becomes increasingly easier to obtain multi-modal or multi-view data, multi-view clustering has gained much more attention recently. However, many methods learn the affinity matrix from the original data and may lead to unsatisfying results because of the noise in the raw dataset. Besides, some methods neglect the diversity of roles played by different views and take them equally. In this paper, we propose a novel Markov chain algorithm named consensus guided auto-weighted multi-view clustering (CAMC) to tackle these problems. A transition probability matrix is constructed for each view to learn the affinity matrix indirectly to reduce the effects of redundancies and noise in the original data. The consensus transition probability matrix is obtained in an auto-weighted way, in which the optimal weight for each view is gained automatically. Besides, a constrained Laplacian rank is utilized on the consensus transition probability to ensure that the number of the connected components in the Laplacian graph is exactly equal to that of the clusters. Moreover, an optimization strategy based on alternating direction method of multiplier (ADMM) is proposed to solve the problem. The effectiveness of the proposed algorithm is verified on a toy dataset. Extensive experiments on seven real-world datasets with different types show that CAMC outperforms the other eight benchmark algorithms in terms of clustering.