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.

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.

This paper aims at proposing a novel 2D non-linear phase decomposition of images, which performs the image processing tasks better than the traditional Fourier transformation (linear phase decomposition), but further, it has additional mathematical properties allowing more effective image analysis, including adaptive decomposition components and positive instantaneous phase derivatives. 1D unwinding Blaschke decomposition has recently been proposed and studied. Through factorization it expresses arbitrary 1D signal into an infinite linear combination of Blaschke products. It offers fast converging positive frequency decomposition in the form of rational approximation. However, in the multi-dimensional cases the usual factorization mechanism does not work. As a consequence, there is no genuine unwinding decomposition for multi-dimensions. In this study a 2D partial unwinding decomposition based on algebraic transforms reducing multi-dimensions to the 1D case is proposed and analyzed. The result shows that the fast convergence offers efficient image reconstruction. The tensor type decomposing terms are mutually orthogonal, giving rise to 2D positive frequency decomposition. The comparison results show that the proposed method outperforms the standard greedy algorithm and the most commonly used methods in the Fourier category. An application in watermarking is presented to demonstrate its potential in applications.

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.