Incomplete Multi-View Unsupervised Federated Feature Selection via Cooperative Particle Swarm Optimization and Tensor-Aligned Learning

With the widespread adoption of multi-view data in numerous fields, multi-view unsupervised feature selection (MUFS) has made notable strides in both feature pruning and missing-view completion. Nonetheless, existing MUFS methods typically rely on centralized servers, which cannot meet real-world demands for privacy preservation and distributed learning, and they often suffer from suboptimal solution and weak convergence guarantees. To address these challenges, IMUFFS, an incomplete multi-view unsupervised federated feature selection via cooperative particle swarm optimization (CPSO) and tensor-aligned learning (TAL) is proposed. Specifically, each client executes CPSO-TAL at two stages: (i) an external optimization phase that involves a CPSO, inspired by the co-evolutionary mechanism of hybrid breeding optimization algorithm, performing a global search in the feature space, and (ii) an internal optimization phase that leverages TAL with imputation and CP decomposition, where CP decomposition reduces dimensionality by decomposing the original tensor into a sum of core components, to learn low-dimensional embeddings, while simultaneously updating anchor graphs and view preference weights, thereby harmonizing imputation and representation learning. On the server side, a federated aggregation strategy using adaptive normalized mutual information (NMI) weighting combines the locally optimized feature selection (FS) weights and NMI scores from clients, ensuring privacy while improving the quality of FS and convergence. Extensive experiments on multiple datasets demonstrate that IMUFFS consistently outperforms state-of-the-art methods, yielding more effective and robust FS and enhancing better missing-view completion.