Manifold-based Incomplete Multi-view Clustering via Bi-Consistency Guidance (MIMB) is a novel method for incomplete multi-view clustering (IMVC), which addresses the challenges of clustering data with missing instances across multiple views. The method integrates the recovery of incomplete data with the learning of a consensus representation to fully consider the consistency information among views. MIMB introduces a biconstency guidance strategy, which explores the consistency information from recovered data through reverse regularization and manifold embedding. The core of MIMB is to learn a consensus representation and obtain consistency information from the recovered data. Specifically, MIMB first utilizes a recovery-based matrix factorization approach to simultaneously recover the incomplete instances and learn a consensus representation. Then, MIMB considers the correction between the recovered data and original data through reverse representation regularization of all the views, which can fully explore the hidden consistency information from the recovered data. In addition, MIMB integrates manifold embedding into the entire framework, which can effectively mine the local structure from the consensus representation. MIMB also introduces an adaptive weight term for each view to balance different views and encourage the mining of manifold structures from recovered data. The proposed MIMB method is evaluated on six benchmark datasets, and the results show that MIMB significantly outperforms several state-of-the-art baselines in terms of clustering performance. The method is effective in handling incomplete multi-view data by recovering missing instances and exploring the latent structure of the data. The experimental results demonstrate that MIMB achieves superior clustering performance across various metrics, including accuracy (ACC), normalized mutual information (NMI), and purity. The method is also robust to increasing missing rates, as the clustering performance remains high even when a significant portion of the data is missing. The proposed MIMB method provides a flexible and effective approach for incomplete multi-view clustering, which can be applied to a wide range of real-world applications.Manifold-based Incomplete Multi-view Clustering via Bi-Consistency Guidance (MIMB) is a novel method for incomplete multi-view clustering (IMVC), which addresses the challenges of clustering data with missing instances across multiple views. The method integrates the recovery of incomplete data with the learning of a consensus representation to fully consider the consistency information among views. MIMB introduces a biconstency guidance strategy, which explores the consistency information from recovered data through reverse regularization and manifold embedding. The core of MIMB is to learn a consensus representation and obtain consistency information from the recovered data. Specifically, MIMB first utilizes a recovery-based matrix factorization approach to simultaneously recover the incomplete instances and learn a consensus representation. Then, MIMB considers the correction between the recovered data and original data through reverse representation regularization of all the views, which can fully explore the hidden consistency information from the recovered data. In addition, MIMB integrates manifold embedding into the entire framework, which can effectively mine the local structure from the consensus representation. MIMB also introduces an adaptive weight term for each view to balance different views and encourage the mining of manifold structures from recovered data. The proposed MIMB method is evaluated on six benchmark datasets, and the results show that MIMB significantly outperforms several state-of-the-art baselines in terms of clustering performance. The method is effective in handling incomplete multi-view data by recovering missing instances and exploring the latent structure of the data. The experimental results demonstrate that MIMB achieves superior clustering performance across various metrics, including accuracy (ACC), normalized mutual information (NMI), and purity. The method is also robust to increasing missing rates, as the clustering performance remains high even when a significant portion of the data is missing. The proposed MIMB method provides a flexible and effective approach for incomplete multi-view clustering, which can be applied to a wide range of real-world applications.