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$$L_1$$ -norm nonparallel hyperplane support vector quantile regression
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DOI：10.1007/s13042-026-03278-z.png)
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Abstract
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To address feature selection in high-dimensional datasets with heterogeneity and asymmetry, this paper proposes $$L_1$$ -norm Nonparallel Hyperplane Support Vector Quantile Regression ( $$L_1$$ -NHSVQR). The proposed model incorporates a quantile parameter to capture heterogeneity across the data distribution and simultaneously constructs two nonparallel lower and upper regression functions to reflect asymmetry at each quantile level. Unlike sparse twin support vector regression, $$L_1$$ -NHSVQR maintains consistency in its training and testing procedures. In addition, the $$L_1$$ -norm regularization term endows the model with an inherent feature selection capability. Experimental results demonstrate that $$L_1$$ -NHSVQR not only identifies relevant features but also comprehensively captures both heterogeneity and asymmetry within the data.
Keywords:
Support vector machine
support vector regression
feature selection
nonparallel hyperplane
L_1 -norm regularization
quantile regression
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