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.

M. Tanveer * Department of Mathematics Indian Institute of T echnology Indore mtanveer@iiti.ac.in Abstract --Restricted kernel machines (RKMs) represent a versatile and powerful framework within the kernel machine family, leveraging conjugate feature duality to address a wide range of machine learning tasks, including classification, regression, and feature learning. However, their performance can degrade significantly in the presence of noise and outliers, which compromises robustness and predictive accuracy. In this paper, we propose a novel enhancement to the RKM framework by integrating a class-informed weighted function. This weighting mechanism dynamically adjusts the contribution of individual training points based on their proximity to class centers and class-specific characteristics, thereby mitigating the adverse effects of noisy and outlier data. By incorporating weighted conjugate feature duality and leveraging the Schur complement theorem, we introduce the class-informed restricted kernel machine (CI-RKM), a robust extension of the RKM designed to improve generalization and resilience to data imperfections. Experimental evaluations on benchmark datasets demonstrate that the proposed CI-RKM consistently outperforms existing baselines, achieving superior classification accuracy and enhanced robustness against noise and outliers. Our proposed method establishes a significant advancement in the development of kernel-based learning models, addressing a core challenge in the field.

The random vector functional link (RVFL) network is a prominent classification model with strong generalization ability. However, RVFL treats all samples uniformly, ignoring whether they are pure or noisy, and its scalability is limited due to the need for inverting the entire training matrix. To address these issues, we propose granular ball RVFL (GB-RVFL) model, which uses granular balls (GBs) as inputs instead of training samples. This approach enhances scalability by requiring only the inverse of the GB center matrix and improves robustness against noise and outliers through the coarse granularity of GBs. Furthermore, RVFL overlooks the dataset's geometric structure. To address this, we propose graph embedding GB-RVFL (GE-GB-RVFL) model, which fuses granular computing and graph embedding (GE) to preserve the topological structure of GBs. The proposed GB-RVFL and GE-GB-RVFL models are evaluated on KEEL, UCI, NDC and biomedical datasets, demonstrating superior performance compared to baseline models.

In robotic inspection, joint registration of multiple point clouds is an essential technique for estimating the transformation relationships between measured parts, such as multiple blades in a propeller. However, the presence of noise and outliers in the data can significantly impair the registration performance by affecting the correctness of correspondences. To address this issue, we incorporate local consistency property into the probability-based joint registration method. Specifically, each measured point set is treated as a sample from an unknown Gaussian Mixture Model (GMM), and the registration problem is framed as estimating the probability model. By incorporating local consistency into the optimization process, we enhance the robustness and accuracy of the posterior distributions, which represent the one-to-all correspondences that directly determine the registration results. Effective closed-form solution for transformation and probability parameters are derived with Expectation-Maximization (EM) algorithm. Extensive experiments demonstrate that our method outperforms the existing methods, achieving high accuracy and robustness with the existence of noise and outliers. The code will be available at https://github.com/sulingjie/JPRLC_registration.

The random vector functional link (RVFL) network is well-regarded for its strong generalization capabilities in the field of machine learning. However, its inherent dependencies on the square loss function make it susceptible to noise and outliers. Furthermore, the calculation of RVFL's unknown parameters necessitates matrix inversion of the entire training sample, which constrains its scalability. To address these challenges, we propose the Wave-RVFL, an RVFL model incorporating the wave loss function. We formulate and solve the proposed optimization problem of the Wave-RVFL using the adaptive moment estimation (Adam) algorithm in a way that successfully eliminates the requirement for matrix inversion and significantly enhances scalability. The Wave-RVFL exhibits robustness against noise and outliers by preventing over-penalization of deviations, thereby maintaining a balanced approach to managing noise and outliers. The proposed Wave-RVFL model is evaluated on multiple UCI datasets, both with and without the addition of noise and outliers, across various domains and sizes. Empirical results affirm the superior performance and robustness of the Wave-RVFL compared to baseline models, establishing it as a highly effective and scalable classification solution.

Generalized eigenvalue proximal support vector machine (GEPSVM) has attracted widespread attention due to its simple architecture, rapid execution, and commendable performance. GEPSVM gives equal significance to all samples, thereby diminishing its robustness and efficacy when confronted with real-world datasets containing noise and outliers. In order to reduce the impact of noises and outliers, we propose a novel intuitionistic fuzzy generalized eigenvalue proximal support vector machine (IF-GEPSVM). The proposed IF-GEPSVM assigns the intuitionistic fuzzy score to each training sample based on its location and surroundings in the high-dimensional feature space by using a kernel function. The solution of the IF-GEPSVM optimization problem is obtained by solving a generalized eigenvalue problem. Further, we propose an intuitionistic fuzzy improved GEPSVM (IF-IGEPSVM) by solving the standard eigenvalue decomposition resulting in simpler optimization problems with less computation cost which leads to an efficient intuitionistic fuzzy-based model. We conduct a comprehensive evaluation of the proposed IF-GEPSVM and IF-IGEPSVM models on UCI and KEEL datasets. Moreover, to evaluate the robustness of the proposed IF-GEPSVM and IF-IGEPSVM models, label noise is introduced into some UCI and KEEL datasets. The experimental findings showcase the superior generalization performance of the proposed models when compared to the existing baseline models, both with and without label noise. Our experimental results, supported by rigorous statistical analyses, confirm the superior generalization abilities of the proposed IF-GEPSVM and IF-IGEPSVM models over the baseline models. Furthermore, we implement the proposed IF-GEPSVM and IF-IGEPSVM models on the USPS recognition dataset, yielding promising results that underscore the models' effectiveness in practical and real-world applications.

In robotic inspection of aviation parts, achieving accurate pairwise point cloud registration between scanned and model data is essential. However, noise and outliers generated in robotic scanned data can compromise registration accuracy. To mitigate this challenge, this article proposes a probability-based registration method utilizing Gaussian Mixture Model (GMM) with local consistency constraint. This method converts the registration problem into a model fitting one, constraining the similarity of posterior distributions between neighboring points to enhance correspondence robustness. We employ the Expectation Maximization algorithm iteratively to find optimal rotation matrix and translation vector while obtaining GMM parameters. Both E-step and M-step have closed-form solutions. Simulation and actual experiments confirm the method's effectiveness, reducing root mean square error by 20% despite the presence of noise and outliers. The proposed method excels in robustness and accuracy compared to existing methods.

In the realm of data classification, broad learning system (BLS) has proven to be a potent tool that utilizes a layer-by-layer feed-forward neural network. It consists of feature learning and enhancement segments, working together to extract intricate features from input data. The traditional BLS treats all samples as equally significant, which makes it less robust and less effective for real-world datasets with noises and outliers. To address this issue, we propose the fuzzy BLS (F-BLS) model, which assigns a fuzzy membership value to each training point to reduce the influence of noises and outliers. In assigning the membership value, the F-BLS model solely considers the distance from samples to the class center in the original feature space without incorporating the extent of non-belongingness to a class. We further propose a novel BLS based on intuitionistic fuzzy theory (IF-BLS). The proposed IF-BLS utilizes intuitionistic fuzzy numbers based on fuzzy membership and non-membership values to assign scores to training points in the high-dimensional feature space by using a kernel function. We evaluate the performance of proposed F-BLS and IF-BLS models on 44 UCI benchmark datasets across diverse domains. Furthermore, Gaussian noise is added to some UCI datasets to assess the robustness of the proposed F-BLS and IF-BLS models. Experimental results demonstrate superior generalization performance of the proposed F-BLS and IF-BLS models compared to baseline models, both with and without Gaussian noise. Additionally, we implement the proposed F-BLS and IF-BLS models on the Alzheimers Disease Neuroimaging Initiative (ADNI) dataset, and promising results showcase the models effectiveness in real-world applications. The proposed methods offer a promising solution to enhance the BLS frameworks ability to handle noise and outliers.

Constructing the adjacency graph is fundamental to graph-based clustering. Graph learning in kernel space has shown impressive performance on a number of benchmark data sets. However, its performance is largely determined by the chosen kernel matrix. To address this issue, the previous multiple kernel learning algorithm has been applied to learn an optimal kernel from a group of predefined kernels. This approach might be sensitive to noise and limits the representation ability of the consensus kernel. In contrast to existing methods, we propose to learn a low-rank kernel matrix which exploits the similarity nature of the kernel matrix and seeks an optimal kernel from the neighborhood of candidate kernels. By formulating graph construction and kernel learning in a unified framework, the graph and consensus kernel can be iteratively enhanced by each other. Extensive experimental results validate the efficacy of the proposed method.