Simplex-Gated Tensor-Product Regularization for Multi-View Multi-Label Feature Selection

Multi-view multi-label feature selection requires balancing shared label structure with view-specific predictive information. We propose Simplex-Gated TensorProduct Regularization (SG-TPR), which preserves the underlying linear featureto-label function class while organizing shared task structure through tensorproduct role–filler geometry. Each view-specific mapping combines a stabilized data-driven residual component with a simplex-gated low-rank structural component, where feature-side roles interact with shared label-side fillers. Signed training-label correlations initialize and calibrate the shared label geometry, while joint row-energy sparsity yields a unified global feature ranking. Across seven benchmarks and eight competitive baselines evaluated under a unified protocol, SG-TPR achieves the best cross-dataset average rank on Average Precision, Coverage, Hamming Loss, and Ranking Loss, with 21 first-place and three secondplace results among 28 dataset–metric comparisons. Matched component controls and an independently retuned gate control support the structural branch and adaptive simplex allocation. These results are consistent with the proposed tensorproduct-organized structured regularization while preserving the underlying linear function class.