Regularized Total Least Squares Broad Learning System for Regression

The Broad Learning System (BLS) has been extensively developed and applied across various fields due to its significant advantages, including high efficiency, strong generality, and scalability. However, in practical applications where both inputs and outputs are contaminated by noise, traditional BLS demonstrates suboptimal performance in handling sample data. This study introduces a novel regularized total least squares broad learning system (RTLS-BLS) designed to enhance the robustness of BLS when noisy values are present in both the input and the output of the training set. Initially, the k-support norm is integrated into the BLS-based autoencoder (BLS-AE), embedded within BLS, to extract robust features from the original input data. The BLS-AE equipped with the k-support norm effectively addresses or mitigates issues related to overly sparse (based on L1-norm) or overly dense (based on L2-norm) regularization of extracted features. Subsequently, regularized total least squares (RTLS) are employed to assess the output weights of BLS, further enhancing its robustness. Moreover, simultaneous perturbation measures for the coefficient matrix and the output are provided. Experimental results from two function approximation tasks, eight benchmark regression tasks, and two network interface flow datasets demonstrate that the proposed RTLS-BLS achieves significantly robust performance under noisy conditions compared to other methods.