Energy-based Deep Incomplete Multi-View Clustering

Incomplete multi-view clustering (IMVC) deals with real-world scenarios where certain views are partially missing, posing significant challenges to effective clustering. Most existing IMVC approaches face a trade-off: imputation-free methods suffer from information bias and imbalance, while full-imputation methods risk introducing and propagating noise. To overcome these limitations, we propose Energy-Based Deep Incomplete Multi-View Clustering (Energy-DIMC), a novel selective-imputation framework that leverages energy-based models (EBMs) to guide reliable imputations and robust clustering. EBMs assess data compatibility by assigning lower energy to more coherent structures, effectively modeling complex inter-view and inter-sample dependencies. Inspired by EBMs, Energy-DIMC integrates four key components: 1) a view feature projector that learns view-specific features and projects them into a common feature space; 2) an energy-guided selective imputation module that identifies the most reliable source view for each view based on view energies, and performs feature imputation only when cross-view transfer is feasible, avoiding unreliable imputations; 3) an energy-based representation fusion module that aggregates observed and selectively imputed features across views via a view attention mechanism, generating view-coherent representations; 4) an energy-enhanced contrastive alignment module that enforces consistency between view-specific and view-coherent representations using dual-level energy signals to preserve true positives. Extensive experiments demonstrate that Energy-DIMC outperforms state-of-the-art IMVC methods across diverse missing-view scenarios. The code is available at https://github.com/sunway677/EnergyIMVC.