Cross-view graph matching for incomplete multi-view clustering

Multi-view clustering (MVC) focuses on adaptively partitioning data from diverse sources into the respective groups and has been widely studied under the assumption of complete data. However, real-world applications often encounter a more realistic incomplete multi-view clustering (IMVC) problem, where data samples are missing in certain views. There are two challenges in IMVC: 1) how to reduce the impact of the missing instances; 2) how to effectively extract the consistent information to cluster the multi-view data. To address the challenges, we propose an adaptive graph learning framework for IMVC, which optimizes the missing information to fit the intrinsic structure of each view and clusters the multi-view data by cross-view graph matching. The proposed method mainly consists of three steps. Firstly, owing to the outstanding performance of the intrinsic structure of data, we adapt it to complete the missing data of each view. Secondly, the connection graph of each view from a projection space is adaptively constructed wherein the data points are connected if and only if they belong to the same cluster. Thirdly, we further introduce a cross-view graph matching strategy to appropriately utilize complementary multi-views information and preserve view-specific semantic information. We develop an iterative algorithm for solving the proposed model. Numerical experiments on several standard datasets demonstrate the effectiveness of the proposed method.