Intuitionistic Fuzzy Graph Embedded Random Vector Functional Link with Multiview Learning

Random Vector Functional Link (RVFL) networks provide an efficient randomized learning framework for classification. Existing multi-view RVFL methods utilize complementary information from multiple views. However, preserving view-specific geometric structure, limiting the influence of large prediction residuals, and modeling relationships between multiple views remain challenging. This paper proposes a Residual-Coupled Graph-Embedded Multi-View RVFL model with fleXi guardian loss (XGRVFL-MV) for multi-view classification. The proposed model constructs RVFL representation for each view, incorporates graph embedding with intrinsic and penalty graphs constructed using the Local Fisher Discriminant Analysis weighting scheme. It also uses the bounded and asymmetric FleXi Guardian (XG) loss for residual learning. A residual-coupling term is introduced to encourage consistency among view-specific prediction residuals while preserving view-specific representations. The resulting optimization problem is solved using an inversion-free first-order optimization procedure based on Nesterov accelerated gradient descent. We evaluate the proposed model on UCI, KEEL, AwA, and Corel5k benchmark datasets. Experimental results, together with statistical analyses and hyperparameter sensitivity analyses, show that XGRVFL-MV achieves competitive classification performance compared with the baseline methods across the evaluated benchmark datasets.

The current state-of-the-art (SOTA) deep randomized neural networks, such as deep Random Vector Functional Link (dRVFL) and ensemble deep RVFL (edRVFL), treat all training samples uniformly, which limits their robustness and effectiveness when applied to real-world datasets containing noise and outliers. Furthermore, the propagation of contaminated features across hidden layers negatively influences the decision-making capability of these models. To overcome these limitations, we propose intuitionistic fuzzy dRVFL (IF-dRVFL) and intuitionistic fuzzy edRVFL (IF-edRVFL) frameworks that enhance model robustness. The proposed models unify intuitionistic fuzzy theory to exploit sample neighborhood information in the kernel space by jointly considering membership and non-membership degrees for each sample. Membership degrees are computed based on the distance of samples from their respective class centroids, while non-membership degrees quantify sample heterogeneity within local neighborhoods. These measures are employed to assign adaptive weights to training samples, enabling effective discrimination among clean, noisy, and outlier data points. Extensive experiments conducted on UCI and KEEL benchmark datasets, with and without the presence of Gaussian noise, demonstrate the superiority of the proposed IF-dRVFL and IF-edRVFL models over existing SOTA fuzzy and non-fuzzy approaches. The source code is available at https://github.com/mtanveer1/IF-edRVFL.

Trusted multi-view classification aims to deliver reliable fusion for accurate predictions and has recently attracted substantial attention in both academia and industry. However, existing TMVC methods typically assume strict alignment across different views during both training and testing phases, which is often impractical in real-world scenarios. This limitation motivates us to revisit TMVC and extend it to a more challenging setting: how to mitigate the impact of view conflict (VC) during both training and inference. To tackle this setting, existing TMVC methods suffer from three critical limitations: underestimated uncertainty, misleading decisions, and overfitting to VC. To address these issues, this paper proposes a novel Robust Fuzzy Multi-View Learning (R-FUML) framework grounded in Fuzzy Set Theory. Specifically, R-FUML models network outputs as fuzzy memberships to quantify category credibility and uses an entropy-based method for reliable multi-view fusion. To this end, we present a Robust Multi-view Fusion (RMF) strategy that accounts for both view-specific uncertainty and inter-view conflicts, thereby alleviating the adverse impacts of VC on decision-making. To identify and conquer VC during training, we further design a Robust Learning Against VC (RLVC) framework. RLVC isolates conflicting samples by leveraging neural networks' memory effects and then retrains the model by applying a penalty to these conflicting views. Extensive experiments across eight public datasets demonstrate that R-FUML consistently outperforms 15 state-of-the-art baselines in robustness and uncertainty estimation. The code will be released upon acceptance.