Federated Multi-View Unsupervised Feature Selection via Bio-Inspired Hierarchical-Cognitive Tianji's Horse Racing Optimization and Tensor Learning.

As multi-view datasets expand across diverse practical fields, feature selection (FS) has become an indispensable preparatory stage for machine learning models. Nevertheless, real-world multi-view data is often unlabeled and distributed among isolated clients, posing significant challenges to traditional centralized methods due to privacy concerns and communication constraints. Furthermore, existing centralized and federated approaches frequently suffer from entrapment in local optima and lack robust convergence guarantees. To address these issues, we propose Fed-MUFSHT, a federated framework for multi-view unsupervised FS (MUFS) that integrates tensor learning with a novel metaheuristic optimizer, Hierarchical-Cognitive Tianji's Horse Racing Optimization (HC-THRO). Within the federated learning paradigm, Fed-MUFSHT follows a dual-stage local optimization process. Stage 1 applies HC-THRO, which integrates Hierarchical Competitive Learning and Adaptive Cognitive Mapping to simulate multi-level strategic competition and cognitive adaptation among individuals. This design enhances global exploration, adaptive learning, and fine-grained feature selection in high-dimensional spaces. Stage 2 employs a TL module based on canonical polyadic (CP) decomposition to perform missing-view imputation and refine latent representation learning. At the global level, a privacy-preserving aggregation strategy based on Normalized Mutual Information (NMI) and feature weights enables efficient model coordination without exposing raw data. Comparative experiments on several public benchmark datasets reveal that Fed-MUFSHT maintains clear advantages over strong competing methods, showing better optimization results together with more dependable convergence characteristics. The overall evidence suggests that the proposed approach is both robust and effective for distributed optimization tasks involving privacy protection.