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Asymmetric least squares support vector machine classifiers

Author

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  • Huang, Xiaolin
  • Shi, Lei
  • Suykens, Johan A.K.

Abstract

In the field of classification, the support vector machine (SVM) pursues a large margin between two classes. The margin is usually measured by the minimal distance between two sets, which is related to the hinge loss or the squared hinge loss. However, the minimal value is sensitive to noise and unstable to re-sampling. To overcome this weak point, the expectile value is considered to measure the margin between classes instead of the minimal value. Motivated by the relation between the expectile value and the asymmetric squared loss, an asymmetric least squares SVM (aLS-SVM) is proposed. The proposed aLS-SVM can also be regarded as an extension to the LS-SVM and the L2-SVM. Theoretical analysis and numerical experiments on the aLS-SVM illustrate its insensitivity to noise around the boundary and its stability to re-sampling.

Suggested Citation

  • Huang, Xiaolin & Shi, Lei & Suykens, Johan A.K., 2014. "Asymmetric least squares support vector machine classifiers," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 395-405.
    • Handle: RePEc:eee:csdana:v:70:y:2014:i:c:p:395-405
    DOI: 10.1016/j.csda.2013.09.015
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    3. Farooq, Muhammad & Steinwart, Ingo, 2017. "An SVM-like approach for expectile regression," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 159-181.
    4. Haoran Zhao & Sen Guo & Huiru Zhao, 2017. "Energy-Related CO 2 Emissions Forecasting Using an Improved LSSVM Model Optimized by Whale Optimization Algorithm," Energies, MDPI, vol. 10(7), pages 1-15, June.
    5. José A. Sáez, 2022. "Noise Models in Classification: Unified Nomenclature, Extended Taxonomy and Pragmatic Categorization," Mathematics, MDPI, vol. 10(20), pages 1-20, October.
    6. Huimin Pei & Qiang Lin & Liran Yang & Ping Zhong, 2021. "A novel semi-supervised support vector machine with asymmetric squared loss," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(1), pages 159-191, March.
    7. Huimin Wang & Zhaojun Steven Li, 2022. "An AdaBoost-based tree augmented naive Bayesian classifier for transient stability assessment of power systems," Journal of Risk and Reliability, , vol. 236(3), pages 495-507, June.

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