Weighted Broad Learning System and Its Application in Nonlinear Industrial Process Modeling

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.

Partial Multilabel Learning Using Noise-Tolerant Broad Learning System With Label Enhancement and Dimensionality Reduction

Partial multilabel learning (PML) addresses the issue of noisy supervision, which contains an overcomplete set of candidate labels for each instance with only a valid subset of training data. Using label enhancement techniques, researchers have computed the probability of a label being ground truth. However, enhancing labels in the noisy label space makes it impossible for the existing partial multilabel label enhancement methods to achieve satisfactory results. Besides, few methods simultaneously involve the ambiguity problem, the feature space's redundancy, and the model's efficiency in PML. To address these issues, this article presents a novel joint partial multilabel framework using broad learning systems (namely BLS-PML) with three innovative mechanisms: 1) a trustworthy label space is reconstructed through a novel label enhancement method to avoid the bias caused by noisy labels; 2) a low-dimensional feature space is obtained by a confidence-based dimensionality reduction method to reduce the effect of redundancy in the feature space; and 3) a noise-tolerant BLS is proposed by adding a dimensionality reduction layer and a trustworthy label layer to deal with PML problem. We evaluated it on six real-world and seven synthetic datasets, using eight state-of-the-art partial multilabel algorithms as baselines and six evaluation metrics. Out of 144 experimental scenarios, our method significantly outperforms the baselines by about 80%, demonstrating its robustness and effectiveness in handling partial multilabel tasks.

Dynamic Graph Regularized Broad Learning With Marginal Fisher Representation for Noisy Data Classification

Broad learning system (BLS) is an effective neural network requiring no deep architecture, however it is somehow fragile to noisy data. The previous robust broad models directly map features from the raw data, which inevitably learn useless or even harmful features for data representation when the inputs are corrupted by noise and outliers. To address this concern, a discriminative and robust network named as dynamic graph regularized broad learning (DGBL) with marginal fisher representation is proposed for noisy data classification. Different from the previous works, DGBL eliminates the effect of noise before the random feature mapping by the proposed robust and dynamic marginal fisher analysis (RDMFA) algorithm. The RDMFA is able to extract more robust and informative representations for classification from the latent clean data space with dynamically generated graphs. Furthermore, the dynamic graphs learned from RDMFA are incorporated as regularization terms into the objective of DGBL to enhance the discrimination capacity of the proposed network. Extensive quantitative and qualitative experiments conducted on numerous benchmark datasets demonstrate the superiority of the proposed model compared to several state-of-the-art methods.

Long-duration electrocardiogram classification based on Subspace Search VMD and Fourier Pooling Broad Learning System

Detecting early stages of cardiovascular disease from short-duration Electrocardiogram (ECG) signals is challenging. However, long-duration ECG data are susceptible to various types of noise during acquisition. To tackle the problem, Subspace Search Variational Mode Decomposition (SSVMD) was proposed, which determines the optimal solution by continuously narrowing the parameter subspace and implements data preprocessing by removing baseline drift noise and high-frequency noise modes. In response to the unclear spatial characteristics and excessive data dimension in long-duration ECG data, a Fourier Pooling Broad Learning System (FPBLS) is proposed. FPBLS integrates a Fourier feature layer and a broad pooling layer to express the input data with more obvious features, reducing the data dimension and maintaining effective features. The theory is verified using the MIT-BIH arrhythmia database and achieves better results compared to the latest literature method.

When Broad Learning System Meets Label Noise Learning: A Reweighting Learning Framework

Broad learning system (BLS) is a novel neural network with efficient learning and expansion capacity, but it is sensitive to noise. Accordingly, the existing robust broad models try to suppress noise by assigning each sample an appropriate scalar weight to tune down the contribution of noisy samples in network training. However, they disregard the useful information of the noncorrupted elements hidden in the noisy samples, leading to unsatisfactory performance. To this end, a novel BLS with adaptive reweighting (BLS-AR) strategy is proposed in this article for the classification of data with label noise. Different from the previous works, the BLS-AR learns for each sample a weight vector rather than a scalar weight to indicate the noise degree of each element in the sample, which extends the reweighting strategy from sample level to element level. This enables the proposed network to precisely identify noisy elements and thus highlight the contribution of informative ones to train a more accurate representation model. Thanks to the separability of the model, the proposed network can be divided into several subnetworks, each of which can be trained efficiently. In addition, three corresponding incremental learning algorithms of the BLS-AR are developed for adding new samples or expanding the network. Substantial experiments are conducted to explicate the effectiveness and robustness of the proposed BLS-AR model.

Modal-Regression-Based Broad Learning System for Robust Regression and Classification

A novel neural network, namely, broad learning system (BLS), has shown impressive performance on various regression and classification tasks. Nevertheless, most BLS models may suffer serious performance degradation for contaminated data, since they are derived under the least-squares criterion which is sensitive to noise and outliers. To enhance the model robustness, in this article we proposed a modal-regression-based BLS (MRBLS) to tackle the regression and classification tasks of data corrupted by noise and outliers. Specifically, modal regression is adopted to train the output weights instead of the minimum mean square error (MMSE) criterion. Moreover, the l2,1 -norm-induced constraint is used to encourage row sparsity of the connection weight matrix and achieve feature selection. To effectively and efficiently train the network, the half-quadratic theory is used to optimize MRBLS. The validity and robustness of the proposed method are verified on various regression and classification datasets. The experimental results demonstrate that the proposed MRBLS achieves better performance than the existing state-of-the-art BLS methods in terms of both accuracy and robustness.

Broad Learning System under Label Noise: A Novel Reweighting Framework with Logarithm Kernel and Mixture Autoencoder

The Broad Learning System (BLS) has demonstrated strong performance across a variety of problems. However, BLS based on the Minimum Mean Square Error (MMSE) criterion is highly sensitive to label noise. To enhance the robustness of BLS in environments with label noise, a function called Logarithm Kernel (LK) is designed to reweight the samples for outputting weights during the training of BLS in order to construct a Logarithm Kernel-based BLS (L-BLS) in this paper. Additionally, for image databases with numerous features, a Mixture Autoencoder (MAE) is designed to construct more representative feature nodes of BLS in complex label noise environments. For the MAE, two corresponding versions of BLS, MAEBLS, and L-MAEBLS were also developed. The extensive experiments validate the robustness and effectiveness of the proposed L-BLS, and MAE can provide more representative feature nodes for the corresponding version of BLS.

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.

Industrial Process Monitoring Based on Dynamic Overcomplete Broad Learning Network

Most industrial processes feature high nonlinearity, non-Gaussianity, and time correlation. Models based on overcomplete broad learning system (OBLS) have been successfully applied in the fault monitoring realm, which may relatively deal with the nonlinear and non-Gaussian characteristics. However, these models barely take time correlation into full consideration, hindering the further improvement of the monitoring accuracy of the network. Therefore, an effective dynamic overcomplete broad learning system (DOBLS) based on matrix extension is proposed, which extends the raw data in the batch process with the idea of "time lag" in this article. Subsequently, the OBLS monitoring network is employed to continue the analysis of the extended dynamic input data. Finally, a monitoring model is established to tackle the coexistence of nonlinearity, non-Gaussianity, and time correlation in process data. To illustrate the superiority and feasibility, the proposed model is conducted on the penicillin fermentation simulation platform, the experimental result of which illustrates that the model can extract the feature of process data more comprehensively and be self-updated more efficiently. With shorter training time and higher monitoring accuracy, the proposed model can witness an improvement of average monitoring accuracy by 3.69% and 1.26% in 26 process fault types compared to the state-of-the-art fault monitoring methods BLS and OBLS, respectively.

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 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.

BLCov: A novel collaborative-competitive broad learning system for COVID-19 detection from radiology images

With the global outbreak of COVID-19, there is an urgent need to develop an effective and automated detection approach as a faster diagnostic alternative to avoid the spread of COVID-19. Recently, broad learning system (BLS) has been viewed as an alternative method of deep learning which has been applied to many areas. Nevertheless, the sparse autoencoder in classical BLS just considers the representations to reconstruct the input data but ignores the relationship among the extracted features. In this paper, inspired by the effectiveness of the collaborative-competitive representation (CCR) mechanism, a novel collaborative-competitive representation-based autoencoder (CCRAE) is first proposed, and then collaborative-competitive broad learning system (CCBLS) is proposed based on CCRAE to effectively address the issues mentioned above. Moreover, an automated CCBLS-based approach is proposed for COVID-19 detection from radiology images such as CT scans and chest X-ray images. In the proposed approach, a feature extraction module is utilized to extract features from CT scans or chest X-ray images, then we use these features for COVID-19 detection with CCBLS. The experimental results demonstrated that our proposed approach can achieve superior or comparable performance in comparison with ten other state-of-the-art methods.

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.

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.

FBLS-Based Fusion Method for Unmanned Surface Vessel Positioning Considering Denoising Algorithm

Although a USV navigation system is an important application of unmanned systems, combining Inertial Navigation System (INS) with Global Positioning System (GPS) can provide reliable and continuous solutions of positioning and navigation based on its several advantages; the random error characteristics of INS and the instability derived from the GPS signal blockage represent a potential threat to the INS/GPS integration of USV. Under this background, a composition framework based on nonlinear generalization capability of support vector machines (SVM) and multi-resolution ability of wavelet transform is used to solve the difficulty that the INS suffers from the interference of stochastic errors, and the dynamic information of the USV is not influenced. An innovative fuzzy broad learning structure based on the broad learning (BL) method is utilized in the INS/GPS integration of USV, in which the navigation information of INS and GPS are deemed as the input of the Fuzzy Broad Learning System (FBLS) to train the network, and then the trained network of FBLS and navigation information of INS are applied for estimating the optimal navigation solution during the GPS signal blockage. Based on the USV platform, a sea trial was carried out to confirm the validity and feasibility of the proposed method by comparing with existing algorithms for INS/GPS integration. The experimental results show that the proposed approach could achieve the better denoising effect from random errors of INS and provide high-accuracy navigation solutions during GPS signal blockage.

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.

Cost-Sensitive Broad Learning System for Imbalanced Classification and Its Medical Application

As an effective and efficient discriminative learning method, the broad learning system (BLS) has received increasing attention due to its outstanding performance without large computational resources. The standard BLS is derived under the minimum mean square error (MMSE) criterion, while MMSE is with poor performance when dealing with imbalanced data. However, imbalanced data are widely encountered in real-world applications. To address this issue, a novel cost-sensitive BLS algorithm (CS-BLS) is proposed. In the CS-BLS, many variations can be adopted, and CS-BLS with weighted cross-entropy is analyzed in this paper. Weighted penalty factors are used in CS-BLS to constrain the contribution of each sample in different classes. The samples in minor classes are allocated higher weights to increase their contributions. Four different weight calculation methods are adopted to the CS-BLS, and thus, four CS-BLS methods are proposed: Log-CS-BLS, Lin-CS-BLS, Sqr-CS-BLS, and EN-CS-BLS. Experiments based on artificially imbalanced datasets of MNIST and small NORB are firstly conducted and compared with the standard BLS. The results show that the proposed CS-BLS methods have better generalization and robustness than the standard BLS. Then, experiments on a real ultrasound breast image dataset are conducted, and the results demonstrate that the proposed CS-BLS methods are effective in actual medical diagnosis.

Broad Learning System Based on Maximum Correntropy Criterion

As an effective and efficient discriminative learning method, broad learning system (BLS) has received increasing attention due to its outstanding performance in various regression and classification problems. However, the standard BLS is derived under the minimum mean square error (MMSE) criterion, which is, of course, not always a good choice due to its sensitivity to outliers. To enhance the robustness of BLS, we propose in this work to adopt the maximum correntropy criterion (MCC) to train the output weights, obtaining a correntropy-based BLS (C-BLS). Due to the inherent superiorities of MCC, the proposed C-BLS is expected to achieve excellent robustness to outliers while maintaining the original performance of the standard BLS in the Gaussian or noise-free environment. In addition, three alternative incremental learning algorithms, derived from a weighted regularized least-squares solution rather than pseudoinverse formula, for C-BLS are developed. With the incremental learning algorithms, the system can be updated quickly without the entire retraining process from the beginning when some new samples arrive or the network deems to be expanded. Experiments on various regression and classification data sets are reported to demonstrate the desirable performance of the new methods.

Angiogenic inhibition therapy, a sliding mode control adventure

BACKGROUND AND OBJECTIVE

A sliding mode based inhibitory agent injection law is derived using angiogenic inhibition model of cancer progression which describes the variation of tumor and supporting vasculature volumes in targeted molecular therapies.

METHODS

The closed loop injection laws are derived by applying sliding mode control method which is known as a robust control approach. It is beneficial especially when there are parametric uncertainties in the dynamical model of the plant. In this research plant is represented by angiogenic cancer progression model. Random uncertainties are introduced to the physiological rate constants and simulations are repeated several times to see the deviations in the states and inhibitory agent rates.

RESULTS

Smooth inhibitory agent injection laws are obtained from the developed approach. Several different control configurations reveal that, it is possible to decrease the setup time to 6.1 days. A few of those settings failed to generate a satisfactory result. It appeared also that the sliding surface parameters have a distinct effect on the closed loop performance. Appropriate choice of the sliding surface parameters allows one to have a robust closed loop treatment where the deviation from the nominal response is relatively lower.

DISCUSSION

The lowest setup time obtained in this research is 6.1 days. This appear shorter than other similar studies where the plant is represented by the same or similar models. In the cases where the setup time is relatively shorter, the inhibitory agent injection requirement is higher than the other cases. This result seems larger compared to similar studies however the inhibitory agent stays at high levels for a short duration. In addition, the existence of uncertainty may also lead to an increase in the inhibitory agent rate requirements. Nevertheless, the results of the study reveals that one can reduce the tumor volume in a finite time without the necessity of constant application of high dosage inhibitory agent.