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Structured multicategory support vector machines with analysis of variance decomposition

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  • Yoonkyung Lee
  • Yuwon Kim
  • Sangjun Lee
  • Ja-Yong Koo

Abstract

The support vector machine has been a popular choice of classification method for many applications in machine learning. While it often outperforms other methods in terms of classification accuracy, the implicit nature of its solution renders the support vector machine less attractive in providing insights into the relationship between covariates and classes. Use of structured kernels can remedy the drawback. Borrowing the flexible model-building idea of functional analysis of variance decomposition, we consider multicategory support vector machines with analysis of variance kernels in this paper. An additional penalty is imposed on the sum of weights of functional subspaces, which encourages a sparse representation of the solution. Incorporation of the additional penalty enhances the interpretability of a resulting classifier with often improved accuracy. The proposed method is demonstrated through simulation studies and an application to real data. Copyright 2006, Oxford University Press.

Suggested Citation

  • Yoonkyung Lee & Yuwon Kim & Sangjun Lee & Ja-Yong Koo, 2006. "Structured multicategory support vector machines with analysis of variance decomposition," Biometrika, Biometrika Trust, vol. 93(3), pages 555-571, September.
    • Handle: RePEc:oup:biomet:v:93:y:2006:i:3:p:555-571
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    File URL: http://hdl.handle.net/10.1093/biomet/93.3.555
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    Cited by:

    1. Zhilan Lou & Jun Shao & Menggang Yu, 2018. "Optimal treatment assignment to maximize expected outcome with multiple treatments," Biometrics, The International Biometric Society, vol. 74(2), pages 506-516, June.
    2. Park, Changyi & Koo, Ja-Yong & Kim, Peter T. & Lee, Jae Won, 2008. "Stepwise feature selection using generalized logistic loss," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3709-3718, March.
    3. Hoai An Le Thi & Manh Cuong Nguyen, 2017. "DCA based algorithms for feature selection in multi-class support vector machine," Annals of Operations Research, Springer, vol. 249(1), pages 273-300, February.
    4. Park, Beomjin & Park, Changyi, 2021. "Kernel variable selection for multicategory support vector machines," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    5. Park, Beomjin & Park, Changyi, 2023. "Multiclass Laplacian support vector machine with functional analysis of variance decomposition," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    6. Lee, Sangjun & Park, Changyi & Koo, Ja-Yong, 2011. "Feature selection in the Laplacian support vector machine," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 567-577, January.
    7. Sohn, Insuk & Shim, Jooyong & Hwang, Changha & Kim, Sujong & Lee, Jae Won, 2009. "Informative transcription factor selection using support vector machine-based generalized approximate cross validation criteria," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1727-1735, March.
    8. Chen, Zhen-Yu & Fan, Zhi-Ping & Sun, Minghe, 2012. "A hierarchical multiple kernel support vector machine for customer churn prediction using longitudinal behavioral data," European Journal of Operational Research, Elsevier, vol. 223(2), pages 461-472.

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