Control barrier functions (CBFs) play a crucial role in achieving the safety-critical control of robotic systems theoretically. However, most existing methods rely on the analytical expressions of unsafe state regions, which is often impractical for irregular and dynamic unsafe regions. In this paper, a novel CBF construction approach, called CoIn-SafeLink, is proposed based on cost-sensitive incremental random vector functional-link (RVFL) neural networks. By designing an appropriate cost function, CoIn-SafeLink achieves differentiated sensitivities to safe and unsafe samples, effectively achieving zero false-negative risk in unsafe sample classification. Additionally, an incremental update theorem for CoIn-SafeLink is proposed, enabling precise adjustments in response to changes in the unsafe region. Finally, the gradient analytical expression of the CoIn-SafeLink is provided to calculate the control input. The proposed method is validated on a 3-degree-of-freedom drone attitude control system. Experimental results demonstrate that the method can effectively learn the unsafe region boundaries and rapidly adapt as these regions evolve, with an update speed approximately five times faster than comparison methods. The source code is available at https://github.com/songqiaohu/CoIn-SafeLink.

The domain of machine learning is confronted with a crucial research area known as class imbalance learning, which presents considerable hurdles in the precise classification of minority classes. This issue can result in biased models where the majority class takes precedence in the training process, leading to the underrepresentation of the minority class. The random vector functional link (RVFL) network is a widely-used and effective learning model for classification due to its speed and efficiency. However, it suffers from low accuracy when dealing with imbalanced datasets. To overcome this limitation, we propose a novel graph embedded intuitionistic fuzzy RVFL for class imbalance learning (GE-IFRVFL-CIL) model incorporating a weighting mechanism to handle imbalanced datasets. The proposed GE-IFRVFL-CIL model has a plethora of benefits, such as $(i)$ it leverages graph embedding to extract semantically rich information from the dataset, $(ii)$ it uses intuitionistic fuzzy sets to handle uncertainty and imprecision in the data, $(iii)$ and the most important, it tackles class imbalance learning. The amalgamation of a weighting scheme, graph embedding, and intuitionistic fuzzy sets leads to the superior performance of the proposed model on various benchmark imbalanced datasets, including UCI and KEEL. Furthermore, we implement the proposed GE-IFRVFL-CIL on the ADNI dataset and achieved promising results, demonstrating the model's effectiveness in real-world applications. The proposed method provides a promising solution for handling class imbalance in machine learning and has the potential to be applied to other classification problems.

A Random Vector Functional Link (RVFL) network is a depth-2 neural network with random inner weights and biases. As only the outer weights of such architectures need to be learned, the learning process boils down to a linear optimization task, allowing one to sidestep the pitfalls of nonconvex optimization problems. In this paper, we prove that an RVFL with ReLU activation functions can approximate Lipschitz continuous functions provided its hidden layer is exponentially wide in the input dimension. Although it has been established before that such approximation can be achieved in $L_2$ sense, we prove it for $L_\infty$ approximation error and Gaussian inner weights. To the best of our knowledge, our result is the first of this kind. We give a nonasymptotic lower bound for the number of hidden layer nodes, depending on, among other things, the Lipschitz constant of the target function, the desired accuracy, and the input dimension. Our method of proof is rooted in probability theory and harmonic analysis.

Neural networks have been successfully employed in various domains such as classification, regression and clustering, etc. Generally, the back propagation (BP) based iterative approaches are used to train the neural networks, however, it results in the issues of local minima, sensitivity to learning rate and slow convergence. To overcome these issues, randomization based neural networks such as random vector functional link (RVFL) network have been proposed. RVFL model has several characteristics such as fast training speed, direct links, simple architecture, and universal approximation capability, that make it a viable randomized neural network. This article presents the first comprehensive review of the evolution of RVFL model, which can serve as the extensive summary for the beginners as well as practitioners. We discuss the shallow RVFLs, ensemble RVFLs, deep RVFLs and ensemble deep RVFL models. The variations, improvements and applications of RVFL models are discussed in detail. Moreover, we discuss the different hyperparameter optimization techniques followed in the literature to improve the generalization performance of the RVFL model. Finally, we give potential future research directions/opportunities that can inspire the researchers to improve the RVFL's architecture and learning algorithm further.

Multivariate time series (MTS) prediction plays a key role in many fields such as finance, energy and transport, where each individual time series corresponds to the data collected from a certain data source, so-called channel. A typical pipeline of building an MTS prediction model (PM) consists of selecting a subset of channels among all available ones, extracting features from the selected channels, and building a PM based on the extracted features, where each component involves certain optimization tasks, i.e., selection of channels, feature extraction (FE) methods, and PMs as well as configuration of the selected FE method and PM. Accordingly, pursuing the best prediction performance corresponds to optimizing the pipeline by solving all of its involved optimization problems. This is a non-trivial task due to the vastness of the solution space. Different from most of the existing works which target at optimizing certain components of the pipeline, we propose a novel evolutionary ensemble learning framework to optimize the entire pipeline in a holistic manner. In this framework, a specific pipeline is encoded as a candidate solution and a multi-objective evolutionary algorithm is applied under different population sizes to produce multiple Pareto optimal sets (POSs). Finally, selective ensemble learning is designed to choose the optimal subset of solutions from the POSs and combine them to yield final prediction by using greedy sequential selection and least square methods. We implement the proposed framework and evaluate our implementation on two real-world applications, i.e., electricity consumption prediction and air quality prediction. The performance comparison with state-of-the-art techniques demonstrates the superiority of the proposed approach.

A random vector functional link network (RVFL) is widely used as a universal approximator for classification and regression problems. The big advantage of RVFL is fast training without backpropagation. This is because the weights and biases of hidden nodes are selected randomly and stay untrained. Recently, alternative architectures with randomized learning are developed which differ from RVFL in that they have no direct links and a bias term in the output layer. In this study, we investigate the effect of direct links and output node bias on the regression performance of RVFL. For generating random parameters of hidden nodes we use the classical method and two new methods recently proposed in the literature. We test the RVFL performance on several function approximation problems with target functions of different nature: nonlinear, nonlinear with strong fluctuations, nonlinear with linear component and linear. Surprisingly, we found that the direct links and output node bias do not play an important role in improving RVFL accuracy for typical nonlinear regression problems. Keywords: Random vector functional link network · Neural networks with random hidden nodes · Randomized learning algorithms.

Both neural networks and decision trees are popular machine learning methods and are widely used to solve problems from diverse domains. These two classifiers are commonly used base classifiers in an ensemble framework. In this paper, we first present a new variant of oblique decision tree based on a linear classifier, then construct an ensemble classifier based on the fusion of a fast neural network, random vector functional link network and oblique decision trees. Random Vector Functional Link Network has an elegant closed form solution with extremely short training time. The neural network partitions each training bag (obtained using bagging) at the root level into C subsets where C is the number of classes in the dataset and subsequently, C oblique decision trees are trained on such partitions. The proposed method provides a rich insight into the data by grouping the confusing or hard to classify samples for each class and thus, provides an opportunity to employ fine-grained classification rule over the data. The performance of the ensemble classifier is evaluated on several multi-class datasets where it demonstrates a superior performance compared to other state-of- the-art classifiers.

ECENTLY, Vapnik and Vashist [1] provided a new learning paradigm termed learning using privileged information (LUPI), which is aimed at enhancing the generalization performance of learning algorithms. Generally speaking, in classical supervised learning paradigm, the training data and test data must come from the same distribution. Although in this new learning paradigm the training data is also considered an unbiased representation for the test data, the LUPI provides a set of additional information for the training data during the training stage, which is called privileged information. In the LUPI paradigm, we use the new training set containing privileged information to train a learning algorithm, while the privileged information is not available in the test stage. We note that the new learning paradigm is analogous to human learning process. In class, a teacher can provide some important and helpful information about this course for students, and these information provided by the teacher can help students acquire knowledge better. Therefore, a teacher plays an essential role in human leaning process. The LUPI paradigm resembling the classroom teaching model can achieve better generalization performance than the traditional learning paradigm. The author is with Department of Industrial Engineering and Logistics Management, School of Engineering, Hong Kong University of Science and Technology, Hong Kong 999077, China.(Email:

Neural networks have been widely used as predictive models to fit data distribution, and they could be implemented through learning a collection of samples. In many applications, however, the given dataset may contain noisy samples or outliers which may result in a poor learner model in terms of generalization. This paper contributes to a development of robust stochastic configuration networks (RSCNs) for resolving uncertain data regression problems. RSCNs are built on original stochastic configuration networks with weighted least squares method for evaluating the output weights, and the input weights and biases are incrementally and randomly generated by satisfying with a set of inequality constrains. The kernel density estimation (KDE) method is employed to set the penalty weights for each training samples, so that some negative impacts, caused by noisy data or outliers, on the resulting learner model can be reduced. The alternating optimization technique is applied for updating a RSCN model with improved penalty weights computed from the kernel density estimation function. Performance evaluation is carried out by a function approximation, four benchmark datasets and a case study on engineering application. Comparisons to other robust randomised neural modelling techniques, including the probabilistic robust learning algorithm for neural networks with random weights and improved RVFL networks, indicate that the proposed RSCNs with KDE perform favourably and demonstrate good potential for real-world applications.

Alzheimer's disease (AD) is a genetically complex neurodegenerative disease, which leads to irreversible brain damage, severe cognitive problems and ultimately death. A number of clinical trials and study initiatives have been set up to investigate AD pathology, leading to large amounts of high dimensional heterogeneous data (biomarkers) for analysis. This paper focuses on combining clinical features from different modalities, including medical imaging, cerebrospinal fluid (CSF), etc., to diagnose AD and predict potential progression. Due to privacy and legal issues involved with clinical research, the study cohort (number of patients) is relatively small, compared to thousands of available biomarkers (predictors). We propose a hybrid pathological analysis model, which integrates manifold learning and Random Vector functional-link network (RVFL) so as to achieve better ability to extract discriminant information with limited training materials. Furthermore, we model (current and future) cognitive healthiness as a regression problem about age. By comparing the difference between predicted age and actual age, we manage to show statistical differences between different pathological stages. Verification tests are conducted based on the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. Extensive comparison is made against different machine learning algorithms, i.e. Support Vector Machine (SVM), Random Forest (RF), Decision Tree and Multilayer Perceptron (MLP). Experimental results show that our proposed algorithm achieves better results than the comparison targets, which indicates promising robustness for practical clinical implementation.