<p>Multi-view clustering (MVC) has significantly been developed with the advances in information acquisition technologies. Most of MVC methods benefit from complete observation of all views so that consistent information and complementary information contained in different views can be extracted effectively. However, not all views of instances are always available in practical applications. In addition, existing self-representation learning methods for subspace clustering do not investigate the local structure of incomplete views to their full extent. This paper introduces a novel approach called Locality Adaptive Incomplete Multi-view Subspace Clustering (LAIMSC) to address the aforementioned challenges. Unlike previous incomplete multi-view subspace clustering that the process of local learning and clustering is often separated into two steps, our LAIMSC method seamlessly integrates local learning and subspace clustering into a unified framework, which can effectively capture complementary information from different incomplete views. In the meantime, due to the incompleteness of views, partitions of different views might be pretty different. Consequently, the proposed LAIMSC method generates an optimal partition for each view and then aligns each partition to form a consensus partition. The LAIMSC method demonstrates superior performance compared to current incomplete multi-view clustering algorithms, as validated by extensive experiments conducted on a variety of challenging datasets.</p>