Treffer: Joint noise detection and L2,p-norm metric in least squares twin SVM for robust multiclass classification.

The least squares twin support vector machine (LSTSVM) serves as a foundational framework for binary classification and is widely applied in statistical learning due to its solid theoretical foundation. It also plays a crucial role in advancing research in multiclass classification. However, the presence of noise in real-world datasets often leads to substantial performance degradation, compromising the reliability and generalizability of this model. Given the ubiquitous presence of noise, its influence on the learning of classification hyperplanes warrants rigorous attention. In this paper, we propose a robust multiclass classification model grounded in LSTSVM, designed to mitigate the influence of noisy data. The proposed framework replaces the conventional squared L<subscript>2</subscript>-norm with the more robust L<subscript>2,p</subscript>-norm (0<p≤2), which enhances resilience against noise. Furthermore, we introduce an innovative noise detection mechanism with a transparent physical interpretation, whereby a probabilistic weight is assigned to each sample to quantify its likelihood of being a normal observation. Specifically, normal samples receive a weight of 1, whereas suspected noisy samples receive a weight of 0. To solve the resulting non-convex optimization problem efficiently, we develop an iterative algorithm that adaptively penalizes normal samples exhibiting substantial errors. The convergence property of the algorithm is rigorously analyzed and theoretically supported. Moreover, the model is extended to semi-supervised learning, enabling the effective exploitation of both a limited set of labeled samples and the structural information inherent in numerous unlabeled samples. Finally, extensive experiments on benchmark and image datasets under varying noise levels demonstrate that the proposed approach consistently outperforms existing methods in terms of classification accuracy and robustness, validating its practical effectiveness in noisy multiclass settings.
(Copyright © 2025 Elsevier Ltd. All rights reserved.)

Declaration of competing interest The authors declare that they have no known financial interests or personal relationships that could be perceived as influencing the research presented in this article.