The Robust Supervised Learning Framework: Harmonious Integration of Twin Extreme Learning Machine, Squared Fractional Loss, Capped L2,p-norm Metric, and Fisher Regularization

Zhenxia Xue, Yan Wang, Yuwen Ren, Xinyuan Zhang

As a novel learning algorithm for feedforward neural networks, the twin extreme learning machine (TELM) boasts advantages such as simple structure, few parameters, low complexity, and excellent generalization performance. However, it employs the squared L2-norm metric and an unbounded hinge loss function, which tends to overstate the influence of outliers and subsequently diminishes the robustness of the model. To address this issue, scholars have proposed the bounded capped L2,p-norm metric, which can be flexibly adjusted by varying the p value to adapt to different data and reduce the impact of noise. Therefore, we substitute the metric in the TELM with the capped L2,p-norm metric in this paper. Furthermore, we propose a bounded, smooth, symmetric, and noise-insensitive squared fractional loss (SF-loss) function to replace the hinge loss function in the TELM. Additionally, the TELM neglects statistical information in the data; thus, we incorporate the Fisher regularization term into our model to fully exploit the statistical characteristics of the data. Drawing upon these merits, a squared fractional loss-based robust supervised twin extreme learning machine (SF-RSTELM) model is proposed by integrating the capped L2,p-norm metric, SF-loss, and Fisher regularization term. The model shows significant effectiveness in decreasing the impacts of noise and outliers. However, the proposed model’s non-convexity poses a formidable challenge in the realm of optimization. We use an efficient iterative algorithm to solve it based on the concave-convex procedure (CCCP) algorithm and demonstrate the convergence of the proposed algorithm. Finally, to verify the algorithm’s effectiveness, we conduct experiments on artificial datasets, UCI datasets, image datasets, and NDC large datasets. The experimental results show that our model is able to achieve higher ACC and F1 scores across most datasets, with improvements ranging from 0.28% to 4.5% compared to other state-of-the-art algorithms.