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This paper introduces an asymmetric, robust, bounded, sparse, and smooth (aR) loss function tailored for an $l_1$-norm penalized geometric twin support vector machine (aRSGTSVM) to enhance classification and regression tasks in the presence of noise and redundant features. The aR loss function effectively mitigates label noise and improves stability against feature noise, while the $l_1$-norm penalty facilitates significant feature selection. Experimental results on synthetic and UCI datasets, along with applications in stock market index tracking, demonstrate the superior performance of aRSGTSVM compared to existing methods.
Noise and redundancy in training data can cripple SVM performance, but a novel loss function transforms the geometric twin SVM into a robust feature selector that excels in challenging environments.
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.
