The random vector functional link (RVFL) neural network has shown significant potential in overcoming the constraints of traditional artificial neural networks, such as excessive computation time and suboptimal solutions. However, RVFL faces challenges when dealing with noise and outliers, as it assumes all data samples contribute equally. To address this issue, we propose a novel robust framework, R2VFL, RVFL with Huber weighting function and class probability, which enhances the model’s robustness and adaptability by effectively mitigating the impact of noise and outliers in the training data. The Huber weighting function reduces the influence of outliers, while the class probability mechanism assigns less weight to noisy data points, resulting in a more resilient model. We explore two distinct approaches for calculating class centers within the R2VFL framework: the simple average of all data points in each class and the median of each feature, the later providing a robust alternative by minimizing the effect of extreme values. These approaches give rise to two novel variants of the model—R2VFL-A and R2VFL-M. We extensively evaluate the proposed models on 47 UCI datasets, encompassing both binary and multiclass datasets, and conduct rigorous statistical testing, which confirms the superiority of the proposed models. Notably, the models also demonstrate exceptional performance in classifying EEG signals, highlighting their practical applicability in real-world biomedical domain.

The plane-based classifiers, support vector machine (SVM) and twin support vector machine (TWSVM), are susceptible to the negative impact of noise, outliers, and class imbalance learning (CIL). The concept of intuitionistic fuzzy (IF) addresses the impact of noise and outliers present in the data. However, IF is sensitive to the threshold distance value and calculates the distance of each data point to other points of its class which is computatinally intensive. Moreover, IF assigns the same score value to the data points that have distinct distances from the center of the other class and identical membership values. To address the aforementioned limitations, in this paper, we propose dual center-based intuitionistic fuzzy plane-based classifiers, specifically dual center-based intuitionistic fuzzy support vector machine (DC-IFSVM) and dual center-based intuitionistic fuzzy least square twin support vector machine (DC-IFLSTSVM). The proposed models, DC-IFSVM and DC-IFLSTSVM handle the CIL by associating class-specific terms in the weighting function. The optimization problem of DC-IFLSTSVM is solved using the conjugate gradient (CG) method. We conducted extensive numerical experiments of the proposed DC-IFSVM, DC-IFLSTSVM and baseline models on 54 UCI and KEEL datasets, which resulted in the superiority of the proposed DC-IFLSTSVM. Furthermore, experiments on the BreakHis dataset, focused on classifying benign tumors from malignant tumors, showcased the remarkable performance of the proposed DC-IFLSTSVM. The code for the proposed model can be found on https://github.com/mtanveer1/DC-IFLSTSVM.

The data mining community has a major challenge in classifying datasets with noise, outliers and imbalanced classes. Twin support vector machine (TSVM) is a well-known plane-based learning technique for classification, however, it has poor performance on aforementioned datasets. To address the issue, in this paper, we propose a novel class probability and generalized bell fuzzy twin SVM for imbalanced data (CGFTSVM-ID). The proposed CGFTSVM-ID assigns membership value to the data points by a new membership function called class probability and generalized bell (CPGB) function. The membership function for majority class is a combination of generalized bell (gbell) function, class probability and imbalance ratio. The gbell function suppress the negative impact of outliers in the training data by assigning them less value. The less class probability of the majority class data points denotes their higher possibility to be noise. The imbalance ratio of the classes considered in the membership function tackles the imbalancing issue of the datasets. In order to ensure the importance of minority class samples in model learning, relatively high memberships are assigned to them. Thus, the proposed CPGB function handles the class imbalance learning problem having noise, and outliers. We employ successive overrelaxation technique to solve the proposed optimization problem. The extensive numerical experiments and statistical analysis carried out over imbalanced real-world UCI and KEEL datasets clearly reveal that the proposed CGFTSVM-ID has superior generalization performance in comparison to baseline models. Moreover, the experiments are also conducted on the publicly available ADNI dataset for Alzheimer's disease classification and results demonstrate the superiority of the proposed CGFTSVM-ID. The code for the proposed CGFTSVM-ID can be found onhttps://github.com/mtanveer1/CGFTSVM-ID.

In practical applications, datasets frequently encompass noise, outliers, and imbalanced classes, which can markedly affect a model's generalization performance. Support vector machine (SVM) and its twin variant i.e., TWSVM tend to be biased towards the majority class samples, leading to misclassification of the minority class samples. TWSVM suffers from this biasness as it generates hyperplanes without considering preceding data information. To address the aforementioned issues, we propose bell-shaped fuzzy least square twin support vector machine for imbalance data (BSFLSTSVM-ID). The proposed BSFLSTSVM-ID allocates weight to the majority class samples through a novel membership function, namely, “class probability and bell-shaped” (CPBS). The CPBS function is amalgamation of class probability, bell-shaped function, and imbalance ratio of the dataset. The bell-shaped function's value diminishes as data points move farther away from the class center, reducing the influence of noise or outliers in constructing hyperplanes. To underscore the importance of samples from minority class, a weight of one is assigned to them. Furthermore, the proposed BSFLSTSVM-ID utilizes the conjugate gradient method to handle the challenge of matrix inversion. To demonstrate its effectiveness, we conducted experiments on 59 UCI and KEEL datasets with imbalance ratios from 1 to 72.69. Additionally, we tested the proposed BSFLSTSVM-ID model's scalability on NDC datasets and applied it to diagnosing breast cancer and Alzheimer's disease using the BreakHis and Alzheimer's Disease Neuroimaging Initiative (ADNI) datasets, respectively. The results show that the proposed BSFLSTSVM-ID outperforms baseline models, highlighting its potential for tackling classification challenges in the biomedical domain.