The broad learning system (BLS) is a lightweight neural network known for its efficient learning capabilities; however, it is limited by its reliance on a binary label strategy. Existing label enhancement models primarily focus on increasing the distances between labels from different classes, which inadvertently expands the distance within the same category. For classification tasks, maintaining similarity within the intraclass is essential for ensuring the model's effectiveness. To address this issue, we propose a groupwise label enhancement BLS model that ensures both intraclass similarity and interclass disparity of labels. Specifically, we develop a novel regression target that generalizes existing label enhancement targets in BLS, increasing the distances between labels of different classes while overcoming the constraints imposed by binary labels. Moreover, we design a groupwise constraint to jointly enhance the intraclass similarity and interclass disparity of labels. Additionally, we propose a novel alternating direction method of multipliers-based optimization algorithm to solve our proposed model, ensuring both computational efficiency and theoretical convergence. Experimental results on several public datasets demonstrate the outstanding effectiveness and efficiency of our proposed model compared to other state-of-the-art methods.

The Broad Learning System (BLS) has been established as an effective flat network alternative to Deep Neural Networks (DNNs), delivering high efficiency while achieving competitive accuracy. Despite its advantages, the incremental learning methods of BLS face challenges in stability and computation when expanding with new nodes or input. We introduce two novel incremental learning algorithms based on factorization updates for BLS that optimize node and input additions to overcome these limitations. Our node addition algorithm utilizes QR decomposition and Cholesky factorization, using the update of the Cholesky factor instead of pseudo-inverse computations. For input addition, we propose an iterative Cholesky factor update algorithm. Our algorithms demonstrate not only faster computation compared to the existing BLS but also improved testing accuracy on the MNIST or Fashion-MNIST dataset. This work presents a significant step forward in the practical application and scalability of BLS in various data-dense environments.

Abstract Representation-based methods have found widespread applications in various classification tasks. However, these methods cannot deal effectively with imbalanced data scenarios. They tend to neglect the importance of minority samples, resulting in bias toward the majority class. To address this limitation, we propose a density-based discriminative nonnegative representation approach for imbalanced classification tasks. First, a new class-specific regularization term is incorporated into the framework of a nonnegative representation based classifier (NRC) to reduce the correlation between classes and improve the discrimination ability of the NRC. Second, a weight matrix is generated based on the hybrid density information of each sample’s neighbors and the decision boundary, which can assign larger weights to minority samples and thus reduce the preference for the majority class. Furthermore, the resulting model can be efficiently optimized through the alternating direction method of multipliers. Extensive experimental results demonstrate that our proposed method is superior to numerous state-of-the-art imbalanced learning methods.

Broad learning system (BLS), which emerges as a lightweight network paradigm, has recently attracted great attention for recognition problems due to its good balance between efficiency and accuracy. However, the supervision mechanism in BLS and its variants generally relies on the strict binary label matrix, which imposes limitations on approximation and fails to adequately align with the data distribution. To address this issue, in this article, two novel flexible label-induced BLS models with the manifold manner are proposed, whose notable characteristics are as follows. First, two proposed label relaxation strategies can both enlarge the margins between different categories and simultaneously enhance the diversity within labels. Second, the integration of manifold geometrical criterion enables the models to capture local feature structures, ensuring the obtained flexible labels align better with the similarity between samples. Third, the proposed models can be optimized efficiently with the alternating direction method of multipliers. Each iteration benefits from a closed-form solution, facilitating the optimization process. Extensive experiments and thorough theoretical analysis are intended to show the advantages of our proposed models compared to other state-of-the-art recognition algorithms.

Most of the existing classification systems assume that the data used is high-quality labeled. However, the labeling process in real-world may inevitably introduce corruptions into labels which can confuse the performances of classifiers. In this paper, based on Broad Learning System (BLS), we propose a novel label noise tolerant method to classify the pattern with corrupted labels. The standard BLS has shown promising efficiency and accuracy in general classification, but its learning process is prone to be affected by the noisy labels. Here, by detailed probabilistic analysis, we first give the reason for lacks of robustness in standard BLS. Then a maximum likelihood estimation-based objective function is derived for robust classification. In addition, a manifold regularization term is integrated to preserve the local geometry of data, which makes the model to be more robust and flexible to learn the output weights. Given some basic assumptions on the approximation errors, the obtained model can be transformed to a graph regularized reweighted BLS problem. The negative effects of noisy labels in data can be inhibited adaptively by assigning reasonable weights. Theoretical analysis and extensive experiments are provided to demonstrate the robustness and effectiveness of the proposed robust BLS model, especially for the case of large amounts of noisy labels.

Sparse representation, collaborative representation, and other kinds of representation based classifiers have been extensively applied to face recognition. Specially, lots of experiments demonstrate that collaborative representation exhibits great potential. These existing classifiers generally focus on the single resolution. They do not work well for multiple resolution issues. However, images taken by different cameras in the real world have different resolutions. To deal with multi-resolution issues, this paper proposes a multi-resolution collaborative representation method. It builds multi-resolution training sample matrices and combines the collaborative representation to solve the multi-resolution recognition problem. Comparison experiments show that the proposed method exhibits the best comprehensive performance between all the tested methods.

Broad Learning System (BLS) has achieved good performance in classification and regression problems, and the computational efficiency is especially outstanding. However, there exists various outliers or noise in the sampling data, which puts a robust requirement on the algorithms. Standard BLS is sensitive to the contaminated data because of its composition structure. In this paper, we propose a robust version of BLS called RBLS to improve its generalization on contaminated data modeling. In RBLS, the ℓ2-norm based cost function will be replaced by ℓ1-norm style cost function. The Augmented Lagrange Multiplier (ALM) method is applied to optimize the new model iteratively. The experiments on function approximation and real-world regression demonstrated that the RBLS method has better modeling performance for sampling data with outliers or noise.