Selection-Consistent Completion for Incomplete Multi-View Unsupervised Feature Selection

Incomplete multi-view unsupervised feature selection aims to identify a compact subset of original features when some views are missing. Existing joint methods combine missing-view completion with feature selection, but completion may still rely on features that are ultimately excluded from the selected subset, creating a mismatch between the selected-feature representation and the information used for completion. We introduce selection–completion consistency, which requires missing-view completion to rely only on currently available selected features while allowing richer observed information to provide auxiliary supervision during training. Based on this principle, we propose Selection-Consistent Multi-View Feature Selection (SC-MVFS), which integrates exact-budget feature selection, probabilistic multi-view posterior fusion, and joint learning with a full-input teacher and a selected-input student. A conditional squared-risk decomposition further characterizes the predictive-information difference between selected and fully observed features. Experiments on eight real-world datasets and controlled synthetic data demonstrate competitive clustering performance. Matched controlled experiments further isolate the effect of using consistent feature inputs during training and final completion and identify the conditions under which this consistency becomes more important.