Fuzzy Broad Learning System: A Novel Neuro-Fuzzy Model for Regression and Classification

Unsupervised Feature Selection for High-Order Embedding Learning and Sparse Learning

The majority of the unsupervised feature selection methods usually explore the first-order similarity of the data while ignoring the high-order similarity of the instances, which makes it easy to construct a suboptimal similarity graph. Furthermore, such methods, often are not suitable for performing feature selection due to their high complexity, especially when the dimensionality of the data is high. To address the above issues, a novel method, termed as unsupervised feature selection for high-order embedding learning and sparse learning (UFSHS), is proposed to select useful features. More concretely, UFSHS first takes advantage of the high-order similarity of the original input to construct an optimal similarity graph that accurately reveals the essential geometric structure of high-dimensional data. Furthermore, it constructs a unified framework, integrating high-order embedding learning and sparse learning, to learn an appropriate projection matrix with row sparsity, which helps to select an optimal subset of features. Moreover, we design a novel alternative optimization method that provides different optimization strategies according to the relationship between the number of instances and the dimensionality, respectively, which significantly reduces the computational complexity of the model. Even more amazingly, the proposed optimization strategy is shown to be applicable to ridge regression, broad learning systems and fuzzy systems. Extensive experiments are conducted on nine public datasets to illustrate the superiority and efficiency of our UFSHS.

Broad learning system based on fractional order optimization

Due to its efficient incremental learning performance, the broad learning system (BLS) has received widespread attention in the field of machine learning. Scholars have found in algorithm research that using the maximum correntropy criterion (MCC) can further improves the performance of broad learning in handling outliers. Recent studies have shown that differential equations can be used to represent the forward propagation of deep learning. The BLS based on MCC uses differentiation to optimize parameters, which indicates that differential methods can also be used for BLS optimization. But general methods use integer order differential equations, ignoring system information between integer orders. Due to the long-term memory property of fractional differential equations, this paper innovatively introduces fractional order optimization into the BLS, called FOBLS, to better enhance the data processing capability of the BLS. Firstly, a BLS is constructed using fractional order, incorporating long-term memory characteristics into the weight optimization process. In addition, constructing a dynamic incremental learning system based on fractional order further enhances the ability of network optimization. The experimental results demonstrate the excellent performance of the method proposed in this paper.

An Incremental-Self-Training-Guided Semi-Supervised Broad Learning System

The broad learning system (BLS) has recently been applied in numerous fields. However, it is mainly a supervised learning system and thus not suitable for specific practical applications with a mixture of labeled and unlabeled data. Despite a manifold regularization-based semi-supervised BLS, its performance still requires improvement, because its assumption is not always applicable. Therefore, this article proposes an incremental-self-training-guided semi-supervised BLS (ISTSS-BLS). Distinctive to traditional self-training, where all unlabeled data are labeled simultaneously, incremental self-training (IST) obtains unlabeled data incrementally from an established sorted list based on the distance between the data and their cluster center. During iterative learning, a small portion of labeled data is first used to train BLS. The system recursively self-updates its structure and meta-parameters using: 1) the double-restricted mechanism and 2) the dynamic neuron-incremental mechanism. The double-restricted mechanism is beneficial to preventing the introduction of incorrect pseudo-labeled samples, and the dynamic neuron-incremental mechanism guides the self-updating of the network structure effectively based on the training accuracy of the labeled data. These strategies guarantee a parsimonious model during the update. Besides, a novel metric, the accuracy-time ratio (A/T), is proposed to evaluate the model's performance comprehensively regarding time and accuracy. In experimental verifications, ISTSS-BLS performs outstandingly on 11 datasets. Specifically, the IST is compared with the traditional one on three scales data, saving up to 52.02% learning time. In addition, ISTSS-BLS is compared with different state-of-the-art alternatives, and all results indicate that it possesses significant advantages in performance.

Co-Training Broad Siamese-Like Network for Coupled-View Semi-Supervised Learning

Multiview semi-supervised learning is a popular research area in which people utilize cross-view knowledge to overcome the limitation of labeled data in semi-supervised learning. Existing methods mainly utilize deep neural network, which is relatively time-consuming due to the complex network structure and back propagation iterations. In this article, co-training broad Siamese-like network (Co-BSLN) is proposed for coupled-view semi-supervised classification. Co-BSLN learns knowledge from two-view data and can be used for multiview data with the help of feature concatenation. Different from existing deep learning methods, Co-BSLN utilizes a simple shallow network based on broad learning system (BLS) to simplify the network structure and reduce training time. It replaces back propagation iterations with a direct pseudo inverse calculation to further reduce time consumption. In Co-BSLN, different views of the same instance are considered as positive pairs due to cross-view consistency. Predictions of views in positive pairs are used to guide the training of each other through a direct logit vector mapping. Such a design is fast and effectively utilizes cross-view consistency to improve the accuracy of semi-supervised learning. Evaluation results demonstrate that Co-BSLN is able to improve accuracy and reduce training time on popular datasets.

Extreme Fuzzy Broad Learning System: Algorithm, Frequency Principle, and Applications in Classification and Regression

As an effective alternative to deep neural networks, broad learning system (BLS) has attracted more attention due to its efficient and outstanding performance and shorter training process in classification and regression tasks. Nevertheless, the performance of BLS will not continue to increase, but even decrease, as the number of nodes reaches the saturation point and continues to increase. In addition, the previous research on neural networks usually ignored the reason for the good generalization of neural networks. To solve these problems, this article first proposes the Extreme Fuzzy BLS (E-FBLS), a novel cascaded fuzzy BLS, in which multiple fuzzy BLS blocks are grouped or cascaded together. Moreover, the original data is input to each FBLS block rather than the previous blocks. In addition, we use residual learning to illustrate the effectiveness of E-FBLS. From the frequency domain perspective, we also discover the existence of the frequency principle in E-FBLS, which can provide good interpretability for the generalization of the neural network. Experimental results on classical classification and regression datasets show that the accuracy of the proposed E-FBLS is superior to traditional BLS in handling classification and regression tasks. The accuracy improves when the number of blocks increases to some extent. Moreover, we verify the frequency principle of E-FBLS that E-FBLS can obtain the low-frequency components quickly, while the high-frequency components are gradually adjusted as the number of FBLS blocks increases.

An Online Evaluation Method for Random Number Entropy Sources Based on Time-Frequency Feature Fusion

Traditional entropy source evaluation methods rely on statistical analysis and are hard to deploy on-chip or online. However, online detection of entropy source quality is necessary in some applications with high encryption levels. To address these issues, our experimental results demonstrate a significant negative correlation between minimum entropy values and prediction accuracy, with a Pearson correlation coefficient of -0.925 (p-value = 1.07 × 10-7). This finding offers a novel approach for assessing entropy source quality, achieving an accurate rate in predicting the next bit of a random sequence using neural networks. To further improve prediction capabilities, we also propose a novel deep learning architecture, Fast Fourier Transform-Attention Mechanism-Long Short-Term Memory Network (FFT-ATT-LSTM), that integrates a simplified soft attention mechanism with Fast Fourier Transform (FFT), enabling effective fusion of time-domain and frequency-domain features. The FFT-ATT-LSTM improves prediction accuracy by 4.46% and 8% over baseline networks when predicting random numbers. Additionally, FFT-ATT-LSTM maintains a compact parameter size of 33.90 KB, significantly smaller than Temporal Convolutional Networks (TCN) at 41.51 KB and Transformers at 61.51 KB, while retaining comparable prediction performance. This optimal balance between accuracy and resource efficiency makes FFT-ATT-LSTM suitable for online deployment, demonstrating considerable application potential.

Bidimensionally partitioned online sequential broad learning system for large-scale data stream modeling

Incremental broad learning system (IBLS) is an effective and efficient incremental learning method based on broad learning paradigm. Owing to its streamlined network architecture and flexible dynamic update scheme, IBLS can achieve rapid incremental reconstruction on the basis of the previous model without the entire retraining from scratch, which enables it adept at handling streaming data. However, two prominent deficiencies still persist in IBLS and constrain its further promotion in large-scale data stream scenarios. Firstly, IBLS needs to retain all historical data and perform associated calculations in the incremental learning process, which causes its computational overhead and storage burden to increase over time and as such puts the efficacy of the algorithm at risk for massive or unlimited data streams. Additionally, due to the random generation rule of hidden nodes, IBLS generally necessitates a large network size to guarantee approximation accuracy, and the resulting high-dimensional matrix calculation poses a greater challenge to the updating efficiency of the model. To address these issues, we propose a novel bidimensionally partitioned online sequential broad learning system (BPOSBLS) in this paper. The core idea of BPOSBLS is to partition the high-dimensional broad feature matrix bidimensionally from the aspects of instance dimension and feature dimension, and consequently decompose a large least squares problem into multiple smaller ones, which can then be solved individually. By doing so, the scale and computational complexity of the original high-order model are substantially diminished, thus significantly improving its learning efficiency and usability for large-scale complex learning tasks. Meanwhile, an ingenious recursive computation method called partitioned recursive least squares is devised to solve the BPOSBLS. This method exclusively utilizes the current online samples for iterative updating, while disregarding the previous historical samples, thereby rendering BPOSBLS a lightweight online sequential learning algorithm with consistently low computational costs and storage requirements. Theoretical analyses and simulation experiments demonstrate the effectiveness and superiority of the proposed algorithm.

Semi-supervised contour-driven broad learning system for autonomous segmentation of concealed prohibited baggage items

With the exponential rise in global air traffic, ensuring swift passenger processing while countering potential security threats has become a paramount concern for aviation security. Although X-ray baggage monitoring is now standard, manual screening has several limitations, including the propensity for errors, and raises concerns about passenger privacy. To address these drawbacks, researchers have leveraged recent advances in deep learning to design threat-segmentation frameworks. However, these models require extensive training data and labour-intensive dense pixel-wise annotations and are finetuned separately for each dataset to account for inter-dataset discrepancies. Hence, this study proposes a semi-supervised contour-driven broad learning system (BLS) for X-ray baggage security threat instance segmentation referred to as C-BLX. The research methodology involved enhancing representation learning and achieving faster training capability to tackle severe occlusion and class imbalance using a single training routine with limited baggage scans. The proposed framework was trained with minimal supervision using resource-efficient image-level labels to localize illegal items in multi-vendor baggage scans. More specifically, the framework generated candidate region segments from the input X-ray scans based on local intensity transition cues, effectively identifying concealed prohibited items without entire baggage scans. The multi-convolutional BLS exploits the rich complementary features extracted from these region segments to predict object categories, including threat and benign classes. The contours corresponding to the region segments predicted as threats were then utilized to yield the segmentation results. The proposed C-BLX system was thoroughly evaluated on three highly imbalanced public datasets and surpassed other competitive approaches in baggage-threat segmentation, yielding 90.04%, 78.92%, and 59.44% in terms of mIoU on GDXray, SIXray, and Compass-XP, respectively. Furthermore, the limitations of the proposed system in extracting precise region segments in intricate noisy settings and potential strategies for overcoming them through post-processing techniques were explored (source code will be available at https://github.com/Divs1159/CNN_BLS .).

Deep Optimized Broad Learning System for Applications in Tabular Data Recognition

The broad learning system (BLS) is a versatile and effective tool for analyzing tabular data. However, the rapid expansion of big data has resulted in an overwhelming amount of tabular data, necessitating the development of specialized tools for effective management and analysis. This article introduces an optimized BLS (OBLS) specifically tailored for big data analysis. In addition, a deep-optimized BLS (DOBLS) network is developed further to enhance the performance and efficiency of the OBLS. The main contributions of this article are: 1) by retracing the network's error from the output space to the latent space, the OBLS adjusts parameters in the feature and enhancement node layers. This process aims to achieve more resilient representations, resulting in improved performance; 2) the DOBLS is a multilayered structure consisting of multiple OBLSs, wherein each OBLS connects to the input and output layers, enabling direct data propagation. This design helps reduce information loss between layers, ensuring an efficient flow of information throughout the network; and 3) the proposed methods demonstrate robustness across various applications, including multiview feature embedding, one-class classification (OCC), camera model identification, electroencephalogram (EEG) signal processing, and radar signal analysis. Experimental results validate the effectiveness of the proposed models. To ensure reproducibility, the source code is available at https://github.com/1027051515/OBLS_DOBLS.

Decoding cognitive health using machine learning: A comprehensive evaluation for diagnosis of significant memory concern

The timely identification of significant memory concern (SMC) is crucial for proactive cognitive health management, especially in an aging population. Detecting SMC early enables timely intervention and personalized care, potentially slowing cognitive disorder progression. This study presents a state‐of‐the‐art review followed by a comprehensive evaluation of machine learning models within the randomized neural networks (RNNs) and hyperplane‐based classifiers (HbCs) family to investigate SMC diagnosis thoroughly. Utilizing the Alzheimer's Disease Neuroimaging Initiative 2 (ADNI2) dataset, 111 individuals with SMC and 111 healthy older adults are analyzed based on T1W magnetic resonance imaging (MRI) scans, extracting rich features. This analysis is based on baseline structural MRI (sMRI) scans, extracting rich features from gray matter (GM), white matter (WM), Jacobian determinant (JD), and cortical thickness (CT) measurements. In RNNs, deep random vector functional link (dRVFL) and ensemble dRVFL (edRVFL) emerge as the best classifiers in terms of performance metrics in the identification of SMC. In HbCs, Kernelized pinball general twin support vector machine (Pin‐GTSVM‐K) excels in CT and WM features, whereas Linear Pin‐GTSVM (Pin‐GTSVM‐L) and Linear intuitionistic fuzzy TSVM (IFTSVM‐L) performs well in the JD and GM features sets, respectively. This comprehensive evaluation emphasizes the critical role of feature selection, feature  based‐interpretability and model choice in attaining an effective classifier for SMC diagnosis. The inclusion of statistical analyses further reinforces the credibility of the results, affirming the rigor of this analysis. The performance measures exhibit the suitability of this framework in aiding researchers with the automated and accurate assessment of SMC. The source codes of the algorithms and datasets used in this study are available at https://github.com/mtanveer1/SMC.

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A Broad Generative Network for Two-Stage Image Outpainting

Image outpainting is a challenge for image processing since it needs to produce a big scenery image from a few patches. In general, two-stage frameworks are utilized to unpack complex tasks and complete them step-by-step. However, the time consumption caused by training two networks will hinder the method from adequately optimizing the parameters of networks with limited iterations. In this article, a broad generative network (BG-Net) for two-stage image outpainting is proposed. As a reconstruction network in the first stage, it can be quickly trained by utilizing ridge regression optimization. In the second stage, a seam line discriminator (SLD) is designed for transition smoothing, which greatly improves the quality of images. Compared with state-of-the-art image outpainting methods, the experimental results on the Wiki-Art and Place365 datasets show that the proposed method achieves the best results under evaluation metrics: the Fréchet inception distance (FID) and the kernel inception distance (KID). The proposed BG-Net has good reconstructive ability with faster training speed than those of deep learning-based networks. It reduces the overall training duration of the two-stage framework to the same level as the one-stage framework. Furthermore, the proposed method is adapted to image recurrent outpainting, demonstrating the powerful associative drawing capability of the model.

Adaptive soft sensor using stacking approximate kernel based BLS for batch processes

To deal with the highly nonlinear and time-varying characteristics of Batch Process, a model named adaptive stacking approximate kernel based broad learning system is proposed in this paper. This model innovatively introduces the approximate kernel based broad learning system (AKBLS) algorithm and the Adaptive Stacking framework, giving it strong nonlinear fitting ability, excellent generalization ability, and adaptive ability. The Broad Learning System (BLS) is known for its shorter training time for effective nonlinear processing, but the uncertainty brought by its double random mapping results in poor resistance to noisy data and unpredictable impact on performance. To address this issue, this paper proposes an AKBLS algorithm that reduces uncertainty, eliminates redundant features, and improves prediction accuracy by projecting feature nodes into the kernel space. It also significantly reduces the computation time of the kernel matrix by searching for approximate kernels to enhance its ability in industrial online applications. Extensive comparative experiments on various public datasets of different sizes validate this. The Adaptive Stacking framework utilizes the Stacking ensemble learning method, which integrates predictions from multiple AKBLS models using a meta-learner to improve generalization. Additionally, by employing the moving window method-where a fixed-length window slides through the database over time-the model gains adaptive ability, allowing it to better respond to gradual changes in industrial Batch Process. Experiments on a substantial dataset of penicillin simulations demonstrate that the proposed model significantly improves predictive accuracy compared to other common algorithms.

BASS: Broad Network Based on Localized Stochastic Sensitivity

The training of the standard broad learning system (BLS) concerns the optimization of its output weights via the minimization of both training mean square error (MSE) and a penalty term. However, it degrades the generalization capability and robustness of BLS when facing complex and noisy environments, especially when small perturbations or noise appear in input data. Therefore, this work proposes a broad network based on localized stochastic sensitivity (BASS) algorithm to tackle the issue of noise or input perturbations from a local perturbation perspective. The localized stochastic sensitivity (LSS) prompts an increase in the network's noise robustness by considering unseen samples located within a Q -neighborhood of training samples, which enhances the generalization capability of BASS with respect to noisy and perturbed data. Then, three incremental learning algorithms are derived to update BASS quickly when new samples arrive or the network is deemed to be expanded, without retraining the entire model. Due to the inherent superiorities of the LSS, extensive experimental results on 13 benchmark datasets show that BASS yields better accuracies on various regression and classification problems. For instance, BASS uses fewer parameters (12.6 million) to yield 1% higher Top-1 accuracy in comparison to AlexNet (60 million) on the large-scale ImageNet (ILSVRC2012) dataset.

Accurate and Efficient Large-Scale Multi-Label Learning With Reduced Feature Broad Learning System Using Label Correlation

Multi-label learning for large-scale data is a grand challenge because of a large number of labels with a complex data structure. Hence, the existing large-scale multi-label methods either have unsatisfactory classification performance or are extremely time-consuming for training utilizing a massive amount of data. A broad learning system (BLS), a flat network with the advantages of succinct structures, is appropriate for addressing large-scale tasks. However, existing BLS models are not directly applicable for large-scale multi-label learning due to the large and complex label space. In this work, a novel multi-label classifier based on BLS (called BLS-MLL) is proposed with two new mechanisms: kernel-based feature reduction module and correlation-based label thresholding. The kernel-based feature reduction module contains three layers, namely, the feature mapping layer, enhancement nodes layer, and feature reduction layer. The feature mapping layer employs elastic network regularization to solve the randomness of features in order to improve performance. In the enhancement nodes layer, the kernel method is applied for high-dimensional nonlinear conversion to achieve high efficiency. The newly constructed feature reduction layer is used to further significantly improve both the training efficiency and accuracy when facing high-dimensionality with abundant or noisy information embedded in large-scale data. The correlation-based label thresholding enables BLS-MLL to generate a label-thresholding function for effective conversion of the final decision values to logical outputs, thus, improving the classification performance. Finally, experimental comparisons among six state-of-the-art multi-label classifiers on ten datasets demonstrate the effectiveness of the proposed BLS-MLL. The results of the classification performance show that BLS-MLL outperforms the compared algorithms in 86% of cases with better training efficiency in 90% of cases.

Evolutionary Weighted Broad Learning and Its Application to Fault Diagnosis in Self-Organizing Cellular Networks

As a novel neural network-based learning framework, a broad learning system (BLS) has attracted much attention due to its excellent performance on regression and balanced classification problems. However, it is found to be unsuitable for imbalanced data classification problems because it treats each class in an imbalanced dataset equally. To address this issue, this work proposes a weighted BLS (WBLS) in which the weight assigned to each class depends on the number of samples in it. In order to further boost its classification performance, an improved differential evolution algorithm is proposed to automatically optimize its parameters, including the ones in BLS and newly generated weights. We first optimize the parameters with a training dataset, and then apply them to WBLS on a test dataset. The experiments on 20 imbalanced classification problems have shown that our proposed method can achieve higher classification accuracy than the other methods in terms of several widely used performance metrics. Finally, it is applied to fault diagnosis in self-organizing cellular networks to further show its applicability to industrial application problems.

Broad learning solution for rapid diagnosis of COVID-19

COVID-19 has put all of humanity in a health dilemma as it spreads rapidly. For many infectious diseases, the delay of detection results leads to the spread of infection and an increase in healthcare costs. COVID-19 diagnostic methods rely on a large number of redundant labeled data and time-consuming data training processes to obtain satisfactory results. However, as a new epidemic, obtaining large clinical datasets is still challenging, which will inhibit the training of deep models. And a model that can really rapidly diagnose COVID-19 at all stages of the model has still not been proposed. To address these limitations, we combine feature attention and broad learning to propose a diagnostic system (FA-BLS) for COVID-19 pulmonary infection, which introduces a broad learning structure to address the slow diagnosis speed of existing deep learning methods. In our network, transfer learning is performed with ResNet50 convolutional modules with fixed weights to extract image features, and the attention mechanism is used to enhance feature representation. After that, feature nodes and enhancement nodes are generated by broad learning with random weights to adaptly select features for diagnosis. Finally, three publicly accessible datasets were used to evaluate our optimization model. It was determined that the FA-BLS model had a 26-130 times faster training speed than deep learning with a similar level of accuracy, which can achieve a fast and accurate diagnosis, achieve effective isolation from COVID-19 and the proposed method also opens up a new method for other types of chest CT image recognition problems.

Overall mortality risk analysis for rectal cancer using deep learning-based fuzzy systems

Colorectal cancer is a leading cause of cancer mortality worldwide, with an increasing incidence rate in developing countries. Integration of genetic information with cancer therapy guidance has shown promise in cancer treatment, indicating its potential as an essential tool in translation oncology. However, the high-throughput analysis and variability of genomic data poses a major challenge to conventional analytic approaches. In this study, we propose an advanced analytic approach, named "Fuzzy-based RNNCoxPH," incorporated fuzzy logic, recurrent neural networks (RNNs), and Cox proportional hazards regression (CoxPH) for detecting missense variants associated with high-risk of all-cause mortality in rectum adenocarcinoma. The test data set was downloaded from "Rectum adenocarcinoma, TCGA-READ" the Genomic Data Commons (GDC) portal. In this study, four model-based risk score models were derived using RNN, CoxPH, RNNCoxPH_Addition, and RNNCoxPH_{Multiplication}. The RNNCoxPH_Addition and RNNCoxPH_{Multiplication} models were obtained as the sum and product of the RNN risk degree matrix and the CoxPH risk degree matrix, respectively. Moreover, the fuzzy logic system was used to calculate the survival risk values of missense variants and classified their membership grade to improve the identification of high-risk gene variation locations associated with cancer mortality. The four models were integrated to develop an advanced risk estimation model. There were 20 028 variants associated with survival status, amongst 17 638 variants were associated with survival and 2390 variants associated with mortality. The proposed Fuzzy-based RNNCoxPH model obtained a balanced accuracy of 93.7%, which was significantly higher than that of the other four test methods. In particular, the CoxPH model is commonly used in medical researches and the XGBoost model is famous for its high accuracy in machine learning. The results suggest that the Fuzzy-based RNNCoxPH model exhibits a higher efficacy in identifying and classifying the missense variants related to mortality risk in rectum adenocarcinoma.

Broad learning for early diagnosis of Alzheimer's disease using FDG-PET of the brain

Alzheimer's disease (AD) is a progressive neurodegenerative disease, and the development of AD is irreversible. However, preventive measures in the presymptomatic stage of AD can effectively slow down deterioration. Fluorodeoxyglucose positron emission tomography (FDG-PET) can detect the metabolism of glucose in patients' brains, which can help to identify changes related to AD before brain damage occurs. Machine learning is useful for early diagnosis of patients with AD using FDG-PET, but it requires a sufficiently large dataset, and it is easy for overfitting to occur in small datasets. Previous studies using machine learning for early diagnosis with FDG-PET have either involved the extraction of elaborately handcrafted features or validation on a small dataset, and few studies have explored the refined classification of early mild cognitive impairment (EMCI) and late mild cognitive impairment (LMCI). This article presents a broad network-based model for early diagnosis of AD (BLADNet) through PET imaging of the brain; this method employs a novel broad neural network to enhance the features of FDG-PET extracted via 2D CNN. BLADNet can search for information over a broad space through the addition of new BLS blocks without retraining of the whole network, thus improving the accuracy of AD classification. Experiments conducted on a dataset containing 2,298 FDG-PET images of 1,045 subjects from the ADNI database demonstrate that our methods are superior to those used in previous studies on early diagnosis of AD with FDG-PET. In particular, our methods achieved state-of-the-art results in EMCI and LMCI classification with FDG-PET.

Forecasting Tourist Arrivals for Hainan Island in China with Decomposed Broad Learning before the COVID-19 Pandemic

This study proposes a decomposed broad learning model to improve the forecasting accuracy for tourism arrivals on Hainan Island in China. With decomposed broad learning, we predicted monthly tourist arrivals from 12 countries to Hainan Island. We compared the actual tourist arrivals to Hainan from the US with the predicted tourist arrivals using three models (FEWT-BL: fuzzy entropy empirical wavelet transform-based broad learning; BL: broad Learning; BPNN: back propagation neural network). The results indicated that US foreigners had the most arrivals in 12 countries, and FEWT-BL had the best performance in forecasting tourism arrivals. In conclusion, we establish a unique model for accurate tourism forecasting that can facilitate decision-making in tourism management, especially at turning points in time.

Dendrite Net: A White-Box Module for Classification, Regression, and System Identification

The simulation of biological dendrite computations is vital for the development of artificial intelligence (AI). This article presents a basic machine-learning (ML) algorithm, called Dendrite Net or DD, just like the support vector machine (SVM) or multilayer perceptron (MLP). DD's main concept is that the algorithm can recognize this class after learning, if the output's logical expression contains the corresponding class's logical relationship among inputs (and \ or \ not). Experiments and main results: DD, a white-box ML algorithm, showed excellent system identification performance for the black-box system. Second, it was verified by nine real-world applications that DD brought better generalization capability relative to the MLP architecture that imitated neurons' cell body (Cell body Net) for regression. Third, by MNIST and FASHION-MNIST datasets, it was verified that DD showed higher testing accuracy under greater training loss than the cell body net for classification. The number of modules can effectively adjust DD's logical expression capacity, which avoids overfitting and makes it easy to get a model with outstanding generalization capability. Finally, repeated experiments in MATLAB and PyTorch (Python) demonstrated that DD was faster than Cell body Net both in epoch and forwardpropagation. The main contribution of this article is the basic ML algorithm (DD) with a white-box attribute, controllable precision for better generalization capability, and lower computational complexity. Not only can DD be used for generalized engineering, but DD has vast development potential as a module for deep learning. DD code is available at https://github.com/liugang1234567/Gang-neuron.

Conditional Joint Distribution-Based Test Selection for Fault Detection and Isolation

Data-driven fault detection and isolation (FDI) depends on complete, comprehensive, and accurate fault information. Optimal test selection can substantially improve information achievement for FDI and reduce the detecting cost and the maintenance cost of the engineering systems. Considerable efforts have been worked to model the test selection problem (TSP), but few of them considered the impact of the measurement uncertainty and the fault occurrence. In this article, a conditional joint distribution (CJD)-based test selection method is proposed to construct an accurate TSP model. In addition, we propose a deep copula function which can describe the dependency among the tests. Afterward, an improved discrete binary particle swarm optimization (IBPSO) algorithm is proposed to deal with TSP. Then, application to an electrical circuit is used to illustrate the efficiency of the proposed method over two available methods: 1) joint distribution-based IBPSO and 2) Bernoulli distribution-based IBPSO.

Adaptive Sensor Fault Accommodation for Vehicle Active Suspensions via Partial Measurement Information

In this article, an adaptive sensor fault accommodation scheme is proposed for uncertain vehicle active suspensions via output-feedback control where vehicle body displacement is the only measurable output signal corrupted by sensor bias. An adaptive observer with variable gains is constructed to obtain state estimates whose design procedure involves parameter adaption of the uncertain system parameters and sensor bias, and an output-feedback controller is designed to attenuate the vehicle body displacement based on the partial measurement information, estimates of the states, and unknown parameters. Compensation for measurement error is made both in the design process of the adaptive observer and output-feedback controller in order to weaken the influence brought about by sensor bias fault. In order to guarantee system stability, the variable observer gains are determined in real time using a switching strategy where their values can be modified in finite times by monitoring the state estimates generated by the observer itself. It is proved that the vehicle body displacement will converge to a small neighborhood around zero, and all the signals of the closed-loop system are ensured to be bounded through selecting suitable control parameters. Simulation is carried out to show the effectiveness of the proposed method and results indicate that better stabilization of the suspension vertical motion can be achieved through adaptive compensation for sensor bias.

Frequency Principle in Broad Learning System

Deep neural networks have achieved breakthrough improvement in various application fields. Nevertheless, they usually suffer from a time-consuming training process because of the complicated structures of neural networks with a huge number of parameters. As an alternative, a fast and efficient discriminative broad learning system (BLS) is proposed, which takes the advantages of flat structure and incremental learning. The BLS has achieved outstanding performance in classification and regression problems. However, the previous studies ignored the reason why the BLS can generalize well. In this article, we focus on the interpretation from the viewpoint of the frequency domain. We discover the existence of the frequency principle in BLS, i.e., the BLS preferentially captures low-frequency components quickly and then fits the high frequencies during the incremental process of adding feature nodes and enhancement nodes. The frequency principle may be of great inspiration for expanding the application of BLS.

Accelerated Log-Regularized Convolutional Transform Learning and Its Convergence Guarantee

Convolutional transform learning (CTL), learning filters by minimizing the data fidelity loss function in an unsupervised way, is becoming very pervasive, resulting from keeping the best of both worlds: the benefit of unsupervised learning and the success of the convolutional neural network. There have been growing interests in developing efficient CTL algorithms. However, developing a convergent and accelerated CTL algorithm with accurate representations simultaneously with proper sparsity is an open problem. This article presents a new CTL framework with a log regularizer that can not only obtain accurate representations but also yield strong sparsity. To efficiently address our nonconvex composite optimization, we propose to employ the proximal difference of the convex algorithm (PDCA) which relies on decomposing the nonconvex regularizer into the difference of two convex parts and then optimizes the convex subproblems. Furthermore, we introduce the extrapolation technology to accelerate the algorithm, leading to a fast and efficient CTL algorithm. In particular, we provide a rigorous convergence analysis for the proposed algorithm under the accelerated PDCA. The experimental results demonstrate that the proposed algorithm can converge more stably to desirable solutions with lower approximation error and simultaneously with stronger sparsity and, thus, learn filters efficiently. Meanwhile, the convergence speed is faster than the existing CTL algorithms.

Face Sketch Synthesis Using Regularized Broad Learning System

There are two main categories of face sketch synthesis: data- and model-driven. The data-driven method synthesizes sketches from training photograph-sketch patches at the cost of detail loss. The model-driven method can preserve more details, but the mapping from photographs to sketches is a time-consuming training process, especially when the deep structures require to be refined. We propose a face sketch synthesis method via regularized broad learning system (RBLS). The broad learning-based system directly transforms photographs into sketches with rich details preserved. Also, the incremental learning scheme of broad learning system (BLS) ensures that our method easily increases feature mappings and remodels the network without retraining when the extracted feature mapping nodes are not sufficient. Besides, a Bayesian estimation-based regularization is introduced with the BLS to aid further feature selection and improve the generalization ability and robustness. Various experiments on the CUHK student data set and Aleix Robert (AR) data set demonstrated the effectiveness and efficiency of our RBLS method. Unlike existing methods, our method synthesizes high-quality face sketches much efficiently and greatly reduces computational complexity both in the training and test processes.

Operating Performance Improvement Based on Prediction and Grade Assessment for Sintering Process

Sintering is the preproduction process of ironmaking, whose products are the basis of ironmaking. How to improve the operating performance of the iron ore sintering process has always been a problem that operators are committed to solve. An operating performance improvement method based on prediction and grade assessment is presented in this article. First, considering the data distribution characteristics of the process, a performance index prediction model based on the Gaussian process regression is built, in which the mutual information analysis method is used to select the inputs of the performance index prediction model. Then, the operating performance grade is assessed by a threshold division method. Next, the operating performance grade guides the control of the burn-through point to improve the operating performance. Finally, experimental verification is performed based on the actual running data. The results show that the proposed method has high prediction accuracy, and it is also significant in improving the operating performance. Therefore, this approach provides an effective solution to predict and improve operating performance.

Type-2 Fuzzy Broad Learning System

The broad learning system (BLS) has been identified as an important research topic in machine learning. However, the typical BLS suffers from poor robustness for uncertainties because of its characteristic of the deterministic representation. To overcome this problem, a type-2 fuzzy BLS (FBLS) is designed and analyzed in this article. First, a group of interval type-2 fuzzy neurons was used to replace the feature neurons of BLS. Then, the representation of BLS can be improved to obtain good robustness. Second, a fuzzy pseudoinverse learning algorithm was designed to adjust the parameter of type-2 FBLS. Then, the proposed type-2 FBLS was able to maintain the fast computational nature of BLS. Third, a theoretical analysis on the convergence of type-2 FBLS was given to show the computational efficiency. Finally, some benchmark and practical problems were used to test the merits of type-2 FBLS. The experimental results indicated that the proposed type-2 FBLS can achieve outstanding performance.

Progressive Ensemble Kernel-Based Broad Learning System for Noisy Data Classification

The broad learning system (BLS) is an algorithm that facilitates feature representation learning and data classification. Although weights of BLS are obtained by analytical computation, which brings better generalization and higher efficiency, BLS suffers from two drawbacks: 1) the performance depends on the number of hidden nodes, which requires manual tuning, and 2) double random mappings bring about the uncertainty, which leads to poor resistance to noise data, as well as unpredictable effects on performance. To address these issues, a kernel-based BLS (KBLS) method is proposed by projecting feature nodes obtained from the first random mapping into kernel space. This manipulation reduces the uncertainty, which contributes to performance improvements with the fixed number of hidden nodes, and indicates that manually tuning is no longer needed. Moreover, to further improve the stability and noise resistance of KBLS, a progressive ensemble framework is proposed, in which the residual of the previous base classifiers is used to train the following base classifier. We conduct comparative experiments against the existing state-of-the-art hierarchical learning methods on multiple noisy real-world datasets. The experimental results indicate our approaches achieve the best or at least comparable performance in terms of accuracy.

PDBL: Improving Histopathological Tissue Classification With Plug-and-Play Pyramidal Deep-Broad Learning

Histopathological tissue classification is a simpler way to achieve semantic segmentation for the whole slide images, which can alleviate the requirement of pixel-level dense annotations. Existing works mostly leverage the popular CNN classification backbones in computer vision to achieve histopathological tissue classification. In this paper, we propose a super lightweight plug-and-play module, named Pyramidal Deep-Broad Learning (PDBL), for any well-trained classification backbone to improve the classification performance without a re-training burden. For each patch, we construct a multi-resolution image pyramid to obtain the pyramidal contextual information. For each level in the pyramid, we extract the multi-scale deep-broad features by our proposed Deep-Broad block (DB-block). We equip PDBL in three popular classification backbones, ShuffLeNetV2, EfficientNetb0, and ResNet50 to evaluate the effectiveness and efficiency of our proposed module on two datasets (Kather Multiclass Dataset and the LC25000 Dataset). Experimental results demonstrate the proposed PDBL can steadily improve the tissue-level classification performance for any CNN backbones, especially for the lightweight models when given a small among of training samples (less than 10%). It greatly saves the computational resources and annotation efforts. The source code is available at: https://github.com/linjiatai/PDBL.

Research Review for Broad Learning System: Algorithms, Theory, and Applications

In recent years, the appearance of the broad learning system (BLS) is poised to revolutionize conventional artificial intelligence methods. It represents a step toward building more efficient and effective machine-learning methods that can be extended to a broader range of necessary research fields. In this survey, we provide a comprehensive overview of the BLS in data mining and neural networks for the first time, focusing on summarizing various BLS methods from the aspects of its algorithms, theories, applications, and future open research questions. First, we introduce the basic pattern of BLS manifestation, the universal approximation capability, and essence from the theoretical perspective. Furthermore, we focus on BLS's various improvements based on the current state of the theoretical research, which further improves its flexibility, stability, and accuracy under general or specific conditions, including classification, regression, semisupervised, and unsupervised tasks. Due to its remarkable efficiency, impressive generalization performance, and easy extendibility, BLS has been applied in different domains. Next, we illustrate BLS's practical advances, such as computer vision, biomedical engineering, control, and natural language processing. Finally, the future open research problems and promising directions for BLSs are pointed out.

Extended Relevance Vector Machine-Based Remaining Useful Life Prediction for DC-Link Capacitor in High-Speed Train

Remaining useful life (RUL) prediction is a reliable tool for the health management of components. The main concern of RUL prediction is how to accurately predict the RUL under uncertainties. In order to enhance the prediction accuracy under uncertain conditions, the relevance vector machine (RVM) is extended into the probability manifold to compensate for the weakness caused by evidence approximation of the RVM. First, tendency features are selected based on the batch samples. Then, a dynamic multistep regression model is built for well describing the influence of uncertainties. Furthermore, the degradation tendency is estimated to monitor degradation status continuously. As poorly estimated hyperparameters of RVM may result in low prediction accuracy, the established RVM model is extended to the probabilistic manifold for estimating the degradation tendency exactly. The RUL is then prognosticated by the first hitting time (FHT) method based on the estimated degradation tendency. The proposed schemes are illustrated by a case study, which investigated the capacitors' performance degradation in traction systems of high-speed trains.

BMT-Net: Broad Multitask Transformer Network for Sentiment Analysis

Sentiment analysis uses a series of automated cognitive methods to determine the author's or speaker's attitudes toward an expressed object or text's overall emotional tendencies. In recent years, the growing scale of opinionated text from social networks has brought significant challenges to humans' sentimental tendency mining. The pretrained language model designed to learn contextual representation achieves better performance than traditional learning word vectors. However, the existing two basic approaches for applying pretrained language models to downstream tasks, feature-based and fine-tuning methods, are usually considered separately. What is more, different sentiment analysis tasks cannot be handled by the single task-specific contextual representation. In light of these pros and cons, we strive to propose a broad multitask transformer network (BMT-Net) to address these problems. BMT-Net takes advantage of both feature-based and fine-tuning methods. It was designed to explore the high-level information of robust and contextual representation. Primarily, our proposed structure can make the learned representations universal across tasks via multitask transformers. In addition, BMT-Net can roundly learn the robust contextual representation utilized by the broad learning system due to its powerful capacity to search for suitable features in deep and broad ways. The experiments were conducted on two popular datasets of binary Stanford Sentiment Treebank (SST-2) and SemEval Sentiment Analysis in Twitter (Twitter). Compared with other state-of-the-art methods, the improved representation with both deep and broad ways is shown to achieve a better F1 -score of 0.778 in Twitter and accuracy of 94.0% in the SST-2 dataset, respectively. These experimental results demonstrate the abilities of recognition in sentiment analysis and highlight the significance of previously overlooked design decisions about searching contextual features in deep and broad spaces.

Improving Video Temporal Consistency via Broad Learning System

Applying image-based processing methods to original videos on a framewise level breaks the temporal consistency between consecutive frames. Traditional video temporal consistency methods reconstruct an original frame containing flickers from corresponding nonflickering frames, but the inaccurate correspondence realized by optical flow restricts their practical use. In this article, we propose a temporally broad learning system (TBLS), an approach that enforces temporal consistency between frames. We establish the TBLS as a flat network comprising the input data, consisting of an original frame in an original video, a corresponding frame in the temporally inconsistent video on which the image-based technique was applied, and an output frame of the last original frame, as mapped features in feature nodes. Then, we refine extracted features by enhancing the mapped features as enhancement nodes with randomly generated weights. We then connect all extracted features to the output layer with a target weight vector. With the target weight vector, we can minimize the temporal information loss between consecutive frames and the video fidelity loss in the output videos. Finally, we remove the temporal inconsistency in the processed video and output a temporally consistent video. Besides, we propose an alternative incremental learning algorithm based on the increment of the mapped feature nodes, enhancement nodes, or input data to improve learning accuracy by a broad expansion. We demonstrate the superiority of our proposed TBLS by conducting extensive experiments.

KAT: A Knowledge Adversarial Training Method for Zero-Order Takagi-Sugeno-Kang Fuzzy Classifiers

While input or output-perturbation-based adversarial training techniques have been exploited to enhance the generalization capability of a variety of nonfuzzy and fuzzy classifiers by means of dynamic regularization, their performance may perhaps be very sensitive to some inappropriate adversarial samples. In order to avoid this weakness and simultaneously ensure enhanced generalization capability, this work attempts to explore a novel knowledge adversarial attack model for the zero-order Tagaki-Sugeno-Kang (TSK) fuzzy classifiers. The proposed model is motivated by exploiting the existence of special knowledge adversarial attacks from the perspective of the human-like thinking process when training an interpretable zero-order TSK fuzzy classifier. Without any direct use of adversarial samples, which is different from input or output perturbation-based adversarial attacks, the proposed model considers adversarial perturbations of interpretable zero-order fuzzy rules in a knowledge-oblivion and/or knowledge-bias or their ensemble to mimic the robust use of knowledge in the human thinking process. Through dynamic regularization, the proposed model is theoretically justified for its strong generalization capability. Accordingly, a novel knowledge adversarial training method called KAT is devised to achieve promising generalization performance, interpretability, and fast training for zero-order TSK fuzzy classifiers. The effectiveness of KAT is manifested by the experimental results on 15 benchmarking UCI and KEEL datasets.

Fuzzy KNN Method With Adaptive Nearest Neighbors

Due to its strong performance in handling uncertain and ambiguous data, the fuzzy k -nearest-neighbor method (FKNN) has realized substantial success in a wide variety of applications. However, its classification performance would be heavily deteriorated if the number k of nearest neighbors was unsuitably fixed for each testing sample. This study examines the feasibility of using only one fixed k value for FKNN on each testing sample. A novel FKNN-based classification method, namely, fuzzy KNN method with adaptive nearest neighbors (A-FKNN), is devised for learning a distinct optimal k value for each testing sample. In the training stage, after applying a sparse representation method on all training samples for reconstruction, A-FKNN learns the optimal k value for each training sample and builds a decision tree (namely, A-FKNN tree) from all training samples with new labels (the learned optimal k values instead of the original labels), in which each leaf node stores the corresponding optimal k value. In the testing stage, A-FKNN identifies the optimal k value for each testing sample by searching the A-FKNN tree and runs FKNN with the optimal k value for each testing sample. Moreover, a fast version of A-FKNN, namely, FA-FKNN, is designed by building the FA-FKNN decision tree, which stores the optimal k value with only a subset of training samples in each leaf node. Experimental results on 32 UCI datasets demonstrate that both A-FKNN and FA-FKNN outperform the compared methods in terms of classification accuracy, and FA-FKNN has a shorter running time.

Weighted Kernel Fuzzy C-Means-Based Broad Learning Model for Time-Series Prediction of Carbon Efficiency in Iron Ore Sintering Process

A key energy consumption in steel metallurgy comes from an iron ore sintering process. Enhancing carbon utilization in this process is important for green manufacturing and energy saving and its prerequisite is a time-series prediction of carbon efficiency. The existing carbon efficiency models usually have a complex structure, leading to a time-consuming training process. In addition, a complete retraining process will be encountered if the models are inaccurate or data change. Analyzing the complex characteristics of the sintering process, we develop an original prediction framework, that is, a weighted kernel-based fuzzy C-means (WKFCM)-based broad learning model (BLM), to achieve fast and effective carbon efficiency modeling. First, sintering parameters affecting carbon efficiency are determined, following the sintering process mechanism. Next, WKFCM clustering is first presented for the identification of multiple operating conditions to better reflect the system dynamics of this process. Then, the BLM is built under each operating condition. Finally, a nearest neighbor criterion is used to determine which BLM is invoked for the time-series prediction of carbon efficiency. Experimental results using actual run data exhibit that, compared with other prediction models, the developed model can more accurately and efficiently achieve the time-series prediction of carbon efficiency. Furthermore, the developed model can also be used for the efficient and effective modeling of other industrial processes due to its flexible structure.

Weighted Generalized Cross-Validation-Based Regularization for Broad Learning System

The broad learning system (BLS) is an emerging flat network, which has demonstrated its outstanding performance in classification and regression problems. The regularization plays an important role in the performance of the BLS. In real applications, since the BLS network is usually expanded dynamically, a predetermined regularization parameter may reduce the performance of the network. Using a fixed regularization in some cases, the classification accuracy of the BLS decreases dramatically when we expand the network. To alleviate this problem, we propose a method that automatically finds appropriate regularization parameters for different datasets, which is based on the weighted generalized cross-validation (WGCV). The experimental results indicate that the WGCV method improves the performance of the BLS, and alleviates the accuracy decrease of the incremental learning algorithm.