cs.LGAug 17, 2026

RoBell-RVFL: A Robust Generalized Bell Random Vector Functional Link Network

Authors: A. Rahaman, A. Quadir, M. Tanveer

Organizations: Department of Mathematics Indian Institute of Technology Indore Indore, India

Read PDF
Ask AI
Cite

Copy citation

DOINot available for this paper

Abstract

The dominance of majority classes in real-world datasets poses a fundamental challenge to randomized neural networks, often biasing decision boundaries and overlooking critical minority samples. Existing remedies, such as synthetic minority over-sampling (SMOTE) and class-weighted loss functions, primarily address class proportions while neglecting intra-class distribution, making them vulnerable to label noise and outliers. In this paper, we propose RoBell-RVFL, a robust and lightweight quality-aware generalized bell random vector functional link network that redefines how randomized models handle class imbalance and noisy data. RoBell-RVFL employs a dual-strategy, sample-level weighting mechanism that strictly preserves minority class information using unit weights, while adaptively regulating the influence of majority class samples through a probability-weighted generalized bell (gbell) membership function in a kernel-induced feature space. This design effectively suppresses noisy, boundary, and outlier samples within the majority class, enabling the network to learn from informative samples rather than merely abundant ones. By explicitly incorporating local class probability and class distribution information into the learning process, RoBell-RVFL achieves adaptive control over sample contributions without sacrificing the closed-form learning efficiency of RVFL networks. Extensive evaluations on UCI and KEEL benchmark datasets, along with robustness tests under up to 40% label noise, demonstrate that RoBell-RVFL consistently and significantly outperforms recent state-of-the-art RVFL variants. The results indicate that adaptive, quality-aware sample weighting is essential for robust RVFL learning, rendering conventional global weighting schemes ineffective in noisy and imbalanced environments.

Figures & tables

Dataset ↓\downarrow | Model →\rightarrowRVFL [ 1 ]RVFLwoDL [ 27 ]NF-RVFL [ 13 ]C-RVFL [ 14 ]AC-RVFL [ 14 ]GB-RVFL [ 15 ]GE-GB-RVFL [ 15 ]RoBell-RVFL †
checkerboard_Data85.942385.980885.576983.173185.576987.019287.019287.5
cleve81.11118082.222273.333381.111175.555682.222283.3333
cmc68.55268.55267.647160.18157.692368.099668.55266.9683
congressional_voting61.068761.068751.908461.068764.122161.068761.068760.3053
conn_bench_sonar_mines_rocks74.603271.428674.603265.079466.666774.603268.25482.5397
crossplane13097.435997.435910079.487289.743610097.435997.4359
Table I : Classification accuracies along with average accuracy and average rankfor RoBell-RVFL model evaluated against baseline models on 26 UCI and KEEL datasets.
Figure S.1 : Architecture of the RVFL neural network.
 RVFLwoDL [ 27 ]RVFL [ 1 ]NF-RVFL [ 30 ]CRVFL [ 14 ]ACRVFL [ 14 ]GB-RVFL [ 15 ]GE-GB-RVFL [ 15 ] 
RVFL [ 1 ][ 9,9,89,9,8 ]       
NF-RVFL [ 30 ][ 16,0,1016,0,10 ][ 15,1,1015,1,10 ]      
C-RVFL [ 14 ][ 10,1,1510,1,15 ][ 8,3,158,3,15 ][ 8,2,168,2,16 ][ 9,2,179,2,17 ]    
AC-RVFL [ 14 ][ 13,2,1113,2,11 ][ 12,3,1112,3,11 ][ 10,2,1410,2,14 ][ 17,5,417,5,4 ]    
GB-RVFL [ 15 ][ 15,4,715,4,7 ][ 17,2,717,2,7 ][ 11,4,1111,4,11 ][ 17,1,817,1,8 ][ 12,5,912,5,9 ]   
GE-GB-RVFL [ 15 ][ 14,4,814,4,8 ][ 15,5,615,5,6 ][ 13,2,1113,2,11 ][ 17,2,717,2,7 ][ 14,3,914,3,9 ][ 11,4,1111,4,11 ]  
Table S.I : Pairwise win-tie-loss test of proposed models and baseline models on MCD category UCI datasets.
 NoiseRoBell-RVFL [ 15 ]RVFL [ 1 ]GB-RVFL [ 15 ]
heart-stat5%85.185285.123554.321
10%90.123582.716186.4198
20%81.481583.950682.7161
30%81.481556.790182.7161
40%49.382750.617377.7778
Average accuracy77.530971.839576.7902
Table S.II : Classification performance of models on different levels of label noise
Figure S.2 : Classification performance plot of models on different levels of label noise.
Figure S.3 : Performance variation of the RoBell-RVFL model with respect to parameters ξ\xi and ρ\rho , respectively.
Figure S.4 : Performance variation of the proposed RoBell-RVFL model with respect to parameters ρ\rho and ξ\xi simultaneously.
IndexActivation Functions
1Scaled Exponential Linear Unit (SELU)
2Rectified Linear Unit (ReLU)
3Sigmoid
4Sine (Sin)
5Hard Limit Transfer Function (Hardlim)
6Triangular Basis Transfer Function (Tribas)
Table S.III : Index of activation functions.
Dataset(Sensitivity, Specificity, Precision, Recall, F-measure, G-mean, γ\gamma , D, Activation, ξ\xi , ρ\rho )
checkerboard_Data(91.2088, 84.6154, 82.1782, 91.2088, 86.4583, 87.8503, 0.01, 163, 6, 2, 1)
cleve(85.3659, 81.6327, 79.5455, 85.3659, 82.3529, 83.4784, 0, 143, 8, 16, 1)
cmc(94.332, 32.3077, 63.8356, 94.332, 76.1438, 55.2055, 100000, 183, 9, 2, 0.625)
congressional_voting(2, 96.2963, 25, 2, 3.7037, 13.8778, 0, 63, 1, 16, 0.625)
conn_bench_sonar_mines_rocks(79.3103, 85.2941, 82.1429, 79.3103, 80.7018, 82.2478, 0.1, 203, 9, 0.125, 0.75)
crossplane130(100, 94.7368, 95.2381, 100, 97.561, 97.3329, 0, 63, 4, 0.0625, 0.5)
Table S.IV : Best hyperparameters and performance of the proposed model for the experiments on 26 UCI [ 31 ] and KEEL [ 32 ] datasets.
More in this topic

Class-Imbalanced Learning

Class-imbalanced learning develops classifiers that recognize rare classes without sacrificing performance on common ones.

See all 256 papers

Explore similar work

CardsList
Aug 13, 2026

Robust Dual-Model Collaborative Random Vector Functional Link Network

Random vector functional link (RVFL) networks are lightweight and fast neural models that offer efficient training and strong generalization through randomized hidden-layer weights and direct input-output connections. However, conventional RVFL models are sensitive to noisy labels, outliers, and imbalanced data, which limits their performance in real-world applications. To address these challenges, we propose the kernel risk-sensitive mean p-power based RVFL (KRPRVFL) model, which integrates the computational efficiency of RVFL with the robustness of the kernel risk-sensitive mean p-power (KRP) criterion. By replacing the standard least-squares objective with a KRP-based loss, KRPRVFL adaptively reduces the influence of corrupted or unreliable samples during training, resulting in improved stability and generalization. Additionally, a collaborative learning mechanism is introduced to enable adaptive interaction among model components, further enhancing robustness in complex and noisy environments. The proposed framework also leverages kernel-induced feature mapping to capture nonlinear relationships without requiring explicit hidden-layer selection, maintaining both efficiency and scalability. Extensive experiments on UCI and KEEL benchmark datasets demonstrate that KRPRVFL consistently outperforms baseline models in terms of accuracy, robustness, and statistical significance, highlighting its effectiveness as a fast, scalable, and reliable solution for challenging classification tasks.

A. Quadir, A. Rahaman, Mushir Akhtar +1

Department of Mathematics Indian Institute of Technology Indore

Learning with Noisy LabelsRobust Loss FunctionsKernel Methods
AskPDF
Aug 30, 2026

GBFRVFL: Granular-Ball Computing-Based Fuzzy Random Vector Functional Link Network

In practical machine learning tasks, data are often contaminated with noise, outliers, and class imbalance, which can degrade the performance of conventional models. While random vector functional link (RVFL) networks offer fast training and strong generalization, they do not explicitly handle uncertainty or exploit local data structure. To address these limitations, we propose a fuzzy granular-ball random vector functional link (GBFRVFL) framework that leverages granular-ball computing to abstract raw samples into adaptive granular balls. Within this framework, we introduce two membership assignment schemes: (i) F-GBRVFL, which incorporates fuzzy membership to quantify the reliability of each granular ball, and (ii) SDAP-GBRVFL, which we propose, incorporates a novel statistical density-adaptive pythagorean membership (SDAPM) scheme that dynamically adjusts membership and non-membership values based on class variance, local sparsity, and granular-ball compactness. These schemes enhance robustness to noise, outliers, class imbalance, and uncertainty in granular-ball distributions, while retaining the computational efficiency of RVFL networks. Extensive experiments on 37 benchmark UCI and KEEL datasets under both clean and noisy conditions demonstrate that the proposed models consistently outperform baseline models, achieving superior accuracy and stability. The results validate the effectiveness of integrating granular-ball computing with adaptive membership schemes for reliable, scalable, and noise-tolerant learning.

A. Quadir, A. Rahaman, P. N. Suganthan +1

Department of Mathematics Indian Institute of Technology Indore · Department of Computer Science and Engineering, College of Engineering Qatar University, Qatar

Neural Network Robustness
AskPDF
Aug 7, 2026

Uncertainty-Aware Ensemble Deep Randomized Neural Networks for Classification

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.

M. Sajid, A. Quadir, A. Rahaman +2

Indian Institute of Technology Indore, Simrol, Indore, India · Qatar University, Qatar

Ensemble LearningNeural Network RobustnessRandom Feature MethodsFuzzy LogicLearning with Noisy Labels
AskPDF