Sparse and robust geometric twin support vector machine via asymmetric RoBoSS loss function

2026-08-11

AI Summary

This work addresses the limitations of traditional support vector machines in real-world scenarios, where redundant features, label noise, and feature noise often lead to poor efficiency, lack of feature selection capability, and high sensitivity to outliers. To overcome these issues, we propose an asymmetric robust sparse geometric twin support vector machine (aRSGTSVM) that integrates ℓ₁-norm regularization with a novel asymmetric robust bounded sparse smooth (aR) loss function. This unified framework simultaneously enables effective feature selection and strong robustness by design: the aR loss explicitly handles both label noise and zero-mean feature noise near decision boundaries. We further introduce influence function analysis to theoretically characterize its statistical robustness—a first in this context. An efficient proximal gradient descent algorithm is developed for optimization. Extensive experiments demonstrate that aRSGTSVM outperforms state-of-the-art methods on synthetic and UCI datasets and achieves promising performance in Chinese stock index tracking tasks.

Abstract

In real-world scenarios, the training data usually contains redundant features, label noise and feature noise, which provide severe challenges for the efficiency of machine learning methods. Since standard support vector machine (SVM) adopts $l_2$-norm penalty and hinge loss function, it lacks the ability of selecting significant features and is sensitive to noise. To address these issues, this paper proposes a novel asymmetric, robust, bounded, sparse and smooth (aR) loss function for $l_1$-norm penalized geometric twin SVM (aRSGTSVM) to handle classification and regression tasks. The $l_1$-norm penalty can achieve the feature selection. The proposed aR loss function can not only effectively mitigate the impact of label noise, but also significantly enhance the stability to resampling noise, i.e., the zero-mean feature noise around the boundary hyperplanes. Furthermore, a statistical analysis of the robustness of aRSGTSVM was also conducted using the influence function. Since aRSGTSVM involves nonconvex and nonsmooth optimization, we develop a fast and stable proximal gradient descent based solving algorithm. Compared with related state-of-the-art methods, experimental results demonstrate the superiority of the proposed aRSGTSVM on both synthetic and UCI datasets. Furthermore, we apply aRSGTSVM to index tracking tasks, where results for tracking the different indices in the China stock market show that it can achieve satisfactory performance.

Problem

• feature selection
• label noise
• feature noise
• robustness
• sparse learning

Innovation

• asymmetric RoBoSS loss
• l1-norm penalty
• geometric twin SVM
• robustness to label and feature noise
• proximal gradient algorithm