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Multi-view data involves various data forms, such as multi-feature, multi-sequence and multimodal data, providing rich semantic information for downstream tasks. The inherent challenge of incomplete multi-view missing multi-label learning lies in how to effectively utilize limited supervision and insufficient data to learn discriminative representation. Starting from the sufficiency of multi-view shared information for downstream tasks, we argue that the existing contrastive learning paradigms on missing multi-view data show limited consistency representation learning ability, leading to the bottleneck in extracting multi-view shared information. In response, we propose to minimize task-independent redundant information by pursuing the maximization of cross-view mutual information. Additionally, to alleviate the hindrance caused by missing labels, we develop a dual-branch soft pseudo-label cross-imputation strategy to improve classification performance. Extensive experiments on multiple benchmarks validate our advantages and demonstrate strong compatibility with both missing and complete data.