Randomized shallow/deep neural networks with closed form solution avoid the shortcomings that exist in the back propagation (BP) based trained neural networks. Ensemble deep random vector functional link (edRVFL) network utilize the strength of two growing fields, i.e., deep learning and ensemble learning. However, edRVFL model doesn't consider the geometrical relationship of the data while calculating the final output parameters corresponding to each layer considered as base model. In the literature, graph embedded frameworks have been successfully used to describe the geometrical relationship within data. In this paper, we propose an extended graph embedded RVFL (EGERVFL) model that, unlike standard RVFL, employs both intrinsic and penalty subspace learning (SL) criteria under the graph embedded framework in its optimization process to calculate the model's output parameters. The proposed shallow EGERVFL model has only single hidden layer and hence, has less representation learning. Therefore, we further develop an ensemble deep EGERVFL (edEGERVFL) model that can be considered a variant of edRVFL model. Unlike edRVFL, the proposed edEGERVFL model solves graph embedded based optimization problem in each layer and hence, has better generalization performance than edRVFL model. We evaluated the proposed approaches for the diagnosis of Alzheimer's disease and furthermore on UCI datasets. The experimental results demonstrate that the proposed models perform better than baseline models. The source code of the proposed models is available at https://github.com/mtanveer1/.

Random vector functional link (RVFL) network has been successfully employed in diverse domains such as computer vision and machine learning, due to its universal approximation capability. Recently, the shallow RVFL architecture has been extended to deep architectures. In deep architectures, multiple hidden layers are stacked for extracting informative features from the original feature space. Therefore, having rich features, deep models are very successful compared to shallow models. In this article, we propose an extended feature RVFL (efRVFL) model that is trained over extended feature space generated analytically from the original feature space. The proposed efRVFL model has three types of features, i.e., original features, supervised randomized (newly generated) features, and unsupervised randomized features, in its feature matrix. The proposed efRVFL model with additional features has capability to capture nonlinear hidden relationships within the dataset. The proposed efRVFL model is an unstable classifier, and thus, its performance can be improved further via ensemble learning. Ensemble models are stable and accurate and have better generalization performance than single models. Therefore, we also propose an ensemble of extended feature RVFL (en-efRVFL) model. Each base model of en-efRVFL is trained over different feature spaces so that more accurate and diverse base models can be generated. The outcome of the base models is integrated via average voting scheme. Empirical evaluation over$46$UCI classification datasets demonstrates that the proposed efRVFL and en-efRVFL models have better performance than RVFL and other given deep models. Furthermore, the experimental results over$12$sparse datasets show that the proposed en-efRVFL model has a winning performance among several deep feedforward neural networks (FNNs).

Alzheimer's disease (AD) is a prominent neurodegenerative disorder, which leads to memory loss and cognitive impairment. The progression is irreversible and shows atrophies in cerebral cortex. Multiple studies revealed that the early diagnosis and early treatment can slow the progress of dementia, and hence, further atrophies can be controlled. Brain imaging data, such as magnetic resonance imaging (MRI), have been prominently used for the diagnosis of AD. Multiple approaches have been proposed for the diagnosis of AD. We propose a novel intuitionistic fuzzy random vector functional link network (IFRVFL) for the diagnosis of AD. Unlike standard random vector functional link (RVFL) network, extreme learning machine (ELM), and kernel ridge regression (KRR), which uses a uniform weighting approach for generating the optimal classifier, the proposed IFRVFL uses a fuzzy weighted approach for generating the optimal classifier. A uniform weighting scheme assumes that all the data samples are equally important; however, in real-world scenarios, this assumption may not hold true due to the presence of outliers and noise. Hence, it results in lower generalization. The proposed IFRVFL assigns each sample an intuitionistic fuzzy number (IFN), which is a function of membership and nonmembership score of a sample. The membership score is a function of the sample distance from the centroid of its corresponding class and the nonmembership score is a function of sample distance from the centroid as well as the neighborhood of the given sample. The proposed IFRVFL effectively reduces the influence of outliers. To evaluate the efficiency of the proposed IFRVFL model, we employed it for the diagnosis of AD. Experimental results demonstrate that the proposed IFRVFL model is superior in mild cognitive impairment (MCI) versus AD case. Thus, IFRVFL can be used in the clinical setting for the early diagnosis of AD. Furthermore, to check the robustness of the proposed IFRVFL model, we also evaluated it on benchmark datasets. Experimental results and the statistical tests reveal that the proposed IFRVFL is better in comparison to baseline models. The source code of the proposed IFRVFL formulation is available at https://github.com/mtanveer1/.

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. However, 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 fuzzy broad learning system (F-BLS) and the intuitionistic fuzzy broad learning system (IF-BLS) models that confront challenges posed by the noise and outliers present in the dataset and enhance overall robustness. Employing a fuzzy membership technique, the proposed F-BLS model embeds sample neighborhood information based on the proximity of each class center within the inherent feature space of the BLS framework. Furthermore, the proposed IF-BLS model introduces intuitionistic fuzzy concepts encompassing membership, non-membership, and score value functions. IF-BLS strategically considers homogeneity and heterogeneity in sample neighborhoods in the kernel space. We evaluate the performance of proposed F-BLS and IF-BLS models on UCI benchmark datasets with and without Gaussian noise. As an application, we implement the proposed F-BLS and IF-BLS models to diagnose Alzheimer's disease (AD). Experimental findings and statistical analyses consistently highlight the superior generalization capabilities of the proposed F-BLS and IF-BLS models over baseline models across all scenarios. The proposed models offer a promising solution to enhance the BLS framework's ability to handle noise and outliers.

The random vector functional link (RVFL) neural network has shown the potential to overcome traditional artificial neural networks’ limitations, such as substantial time consumption and the emergence of suboptimal solutions. However, RVFL struggles to provide comprehensive insights into its decisionmaking processes. We propose the Neuro-fuzzy RVFL (NFRVFL) model by combining RVFL with neuro-fuzzy system. The proposed NF-RVFL model takes human-like decisions based on the IF-THEN approach and enhances its transparency in decision-making. Within this framework, input features undergo a fuzzification process as they traverse the fuzzy layer. The resulting fuzzified features then navigate a hidden layer through random projection as well as yielding defuzzified values via defuzzification. The defuzzified values, hidden layer outputs and original input features collectively contribute to the output prediction process. The proposed NF-RVFL model employs three distinct clustering methods to establish fuzzy layer centers: randomly initialized centers (referred to as Rmeans), K-means clustering centers, and fuzzy C-means clustering centers. This approach generates three distinct model variations, namely NF-RVFL-R, NF-RVFL-K and NF-RVFL-C, each producing a diverse set of fuzzified and defuzzified samples. Our research involves experiments on various UCI benchmark datasets, covering binary, multiclass classification, and regression tasks. These datasets are sourced from diverse domains and exhibit different sizes. We compare the proposed NF-RVFL models to the existing baseline models. The statistical tests and comprehensive experimental analyses across binary, multiclass, and regression datasets consistently show that all variations of the proposed NF-RVFL model outperform baseline models, highlighting their generalization capabilities. The proposed NF-RVFL models show the generic nature by being adeptly applicable and excelling in regression as well as classification tasks. The source code of the proposed NF-RVFL model is available athttps://github.com/mtanveer1/NeuroFuzzy-RVFL.

The domain of machine learning is confronted with a crucial research area known as class imbalance (CI) 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 good generalization performance and efficiency. However, it suffers when dealing with imbalanced datasets. To overcome this limitation, we propose a novel graph-embedded intuitionistic fuzzy RVFL for CI learning (GE-IFRVFL-CIL) model incorporating a weighting mechanism to handle imbalanced datasets. The proposed GE-IFRVFL-CIL model offers a plethora of benefits: 1) leveraging graph embedding (GE) to preserve the inherent topological structure of the datasets; 2) employing intuitionistic fuzzy (IF) theory to handle uncertainty and imprecision in the data; and 3) the most important, it tackles CI learning. The amalgamation of a weighting scheme, GE, and IF sets leads to the superior performance of the proposed models on KEEL benchmark imbalanced datasets with and without Gaussian noise. Furthermore, we implemented the proposed GE-IFRVFL-CIL on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset and achieved promising results, demonstrating the model's effectiveness in real-world applications. The proposed GE-IFRVFL-CIL model offers a promising solution to address the CI issue, mitigates the detrimental effect of noise and outliers, and preserves the inherent geometrical structures of the dataset.

A teacher in a school plays significant role in classroom while teaching the students. Similarly, learning via privileged information (LUPI) gives extra information generated by a teacher to 'teach' the learning algorithm while training. This paper proposes minimum variance embedded random vector functional link network with privileged information (MVRVFL+). The proposed MVRVFL+ minimizes the intraclass variance of the training data and uses privileged information paradigm which provides the additional knowledge during the training of the model. The proposed MVRVFL+ classification model is evaluated on 43 benchmark UCI datasets. From the experimental analysis, the proposed MVRVFL+ showed best average accuracy and emerged as the lowest average rank classifier among the baseline models.

Ensemble learning methods, which combine several base classifiers, is a common technique to enhance the classification ability of ensemble models in the field of pattern recognition and machine learning. Rotation Forest, an ensemble algorithm, has been used widely in various fields with nice generalization performance. The main idea of Rotation Forest is to animate concurrently both diversity and individual accuracy within the ensemble. On the other hand, random vector functional link (RVFL) neural network, a randomized version of single layer feed-forward neural network (SLFN), is a successful model because of its universal approximation property. In this paper, we propose a novel ensemble method, known as rotated random vector functional link neural network (RoF-RVFL), which combines rotation forest (RoF) and RVFL classifiers. To verify the effectiveness of the proposed RoF- RVFL method, empirical comparisons are carried out among Rotation Forest (RoF), Random Forest (RaF), RVFL and the proposed RoF-RVFL method over 42 UCI benchmark datasets. The experimental results show that the proposed RoF-Rvflmethod is able to generate more robust network with better generalization performance.