Fuzzy Reverse Neighborhood Discriminant Analysis: Soft Memberships, Adaptive Graphs, and Choquet-Integral Fusion for Robust Feature Extraction

Conventional linear discriminant analysis (LDA) and its graph-based extensions encounter challenges with class overlap, uneven sampling, and inflexible neighborhood selection. Although reverse nearest neighbor (RNN) graphs address data density, standard Reverse Neighborhood Discriminant Analysis (RNDA) relies on hard labels and binary edges. This work introduces Fuzzy Reverse Neighborhood Discriminant Analysis (FRNDA), which incorporates fuzzy class memberships, multiple fuzzy RNN graphs with smoothly decaying edge weights, and Choquet integral-based regularization to model non-additive interactions. The ℓ2,1-norm is employed to induce joint feature sparsity. Theoretical contributions include a proof of monotonic convergence under supermodularity, a correction to a gradient error in Choquet fusion, and a tighter complexity bound for sparse approximate-neighbor graphs. FRNDA reduces to RNDA in the crisp case and generalizes to matrix inputs as 2DFRNDA. Evaluation on 12 benchmarks, including CIFAR-10, Fashion-MNIST, Caltech-101, Tiny ImageNet, Office-31, and FER2013, demonstrates that FRNDA/2DFRNDA outperforms classical and modern graph-embedding methods on 10 of the 12 datasets. Crisp RNDA remains preferable on Fashion-MNIST (for FRNDA alone) and FER2013, and these exceptions are analyzed. When applied to frozen ResNet-50 and Supervised Contrastive Learning features, FRNDA consistently improves accuracy, supporting its role as a hybrid post-processing method. FRNDA exhibits robustness to Gaussian noise, with only a 3.65-percentage-point drop in accuracy compared to RNDA’s 7.0-percentage-point decrease, and Choquet fusion surpasses linear averaging. Results are consistent across diverse initializations.