IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v249y2017i1d10.1007_s10479-016-2333-y.html
   My bibliography  Save this article

DCA based algorithms for feature selection in multi-class support vector machine

Author

Listed:
  • Hoai An Le Thi

    (Ton Duc Thang University
    University of Lorraine)

  • Manh Cuong Nguyen

    (University of Lorraine)

Abstract

This paper addresses the problem of feature selection for Multi-class Support Vector Machines. Two models involving the $$\ell _{0}$$ ℓ 0 (the zero norm) and the $$\ell _{2}$$ ℓ 2 – $$\ell _{0}$$ ℓ 0 regularizations are considered for which two continuous approaches based on DC (Difference of Convex functions) programming and DCA (DC Algorithms) are investigated. The first is DC approximation via several sparse inducing functions and the second is an exact reformulation approach using penalty techniques. Twelve versions of DCA based algorithms are developed on which empirical computational experiments are fully performed. Numerical results on real-world datasets show the efficiency and the superiority of our methods versus one of the best standard algorithms on both feature selection and classification.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:249:y:2017:i:1:d:10.1007_s10479-016-2333-y
    DOI: 10.1007/s10479-016-2333-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-016-2333-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-016-2333-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Liu, Yufeng & Helen Zhang, Hao & Park, Cheolwoo & Ahn, Jeongyoun, 2007. "Support vector machines with adaptive Lq penalty," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6380-6394, August.
    2. Hoai Le Thi & Tao Pham Dinh & Huynh Ngai, 2012. "Exact penalty and error bounds in DC programming," Journal of Global Optimization, Springer, vol. 52(3), pages 509-535, March.
    3. Hoai Le Thi & Hoai Le & Van Nguyen & Tao Pham Dinh, 2008. "A DC programming approach for feature selection in support vector machines learning," 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. 2(3), pages 259-278, December.
    4. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    5. Wang, Hansheng & Li, Guodong & Jiang, Guohua, 2007. "Robust Regression Shrinkage and Consistent Variable Selection Through the LAD-Lasso," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 347-355, July.
    6. Goller, Daniel & Lechner, Michael & Moczall, Andreas & Wolff, Joachim, 2020. "Does the estimation of the propensity score by machine learning improve matching estimation? The case of Germany's programmes for long term unemployed," Labour Economics, Elsevier, vol. 65(C).
    7. Lee, Yoonkyung & Lin, Yi & Wahba, Grace, 2004. "Multicategory Support Vector Machines: Theory and Application to the Classification of Microarray Data and Satellite Radiance Data," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 67-81, January.
    8. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    9. Le An & Pham Tao, 2005. "The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems," Annals of Operations Research, Springer, vol. 133(1), pages 23-46, January.
    10. Le Thi, H.A. & Pham Dinh, T. & Le, H.M. & Vo, X.T., 2015. "DC approximation approaches for sparse optimization," European Journal of Operational Research, Elsevier, vol. 244(1), pages 26-46.
    11. Hoai An, Le Thi & Minh, Le Hoai & Tao, Pham Dinh, 2007. "Optimization based DC programming and DCA for hierarchical clustering," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1067-1085, December.
    12. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alaleh Razmjoo & Petros Xanthopoulos & Qipeng Phil Zheng, 2019. "Feature importance ranking for classification in mixed online environments," Annals of Operations Research, Springer, vol. 276(1), pages 315-330, May.
    2. M. Tanveer & T. Rajani & R. Rastogi & Y. H. Shao & M. A. Ganaie, 2024. "Comprehensive review on twin support vector machines," Annals of Operations Research, Springer, vol. 339(3), pages 1223-1268, August.
    3. Scindhiya Laxmi & S. K. Gupta & Sumit Kumar, 2024. "Intuitionistic fuzzy least square twin support vector machines for pattern classification," Annals of Operations Research, Springer, vol. 339(3), pages 1329-1378, August.
    4. Hadi Abbaszadehpeivasti & Etienne Klerk & Moslem Zamani, 2024. "On the Rate of Convergence of the Difference-of-Convex Algorithm (DCA)," Journal of Optimization Theory and Applications, Springer, vol. 202(1), pages 475-496, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Le Thi, H.A. & Pham Dinh, T. & Le, H.M. & Vo, X.T., 2015. "DC approximation approaches for sparse optimization," European Journal of Operational Research, Elsevier, vol. 244(1), pages 26-46.
    2. Jun Sun & Wentao Qu, 2022. "DCA for Sparse Quadratic Kernel-Free Least Squares Semi-Supervised Support Vector Machine," Mathematics, MDPI, vol. 10(15), pages 1-17, August.
    3. Umberto Amato & Anestis Antoniadis & Italia De Feis & Irene Gijbels, 2021. "Penalised robust estimators for sparse and high-dimensional linear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 1-48, March.
    4. Jiang, Rong & Qian, Weimin & Zhou, Zhangong, 2012. "Variable selection and coefficient estimation via composite quantile regression with randomly censored data," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 308-317.
    5. Guang Cheng & Hao Zhang & Zuofeng Shang, 2015. "Sparse and efficient estimation for partial spline models with increasing dimension," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 93-127, February.
    6. Bai, Jushan & Liao, Yuan, 2016. "Efficient estimation of approximate factor models via penalized maximum likelihood," Journal of Econometrics, Elsevier, vol. 191(1), pages 1-18.
    7. Hu Yang & Ning Li & Jing Yang, 2020. "A robust and efficient estimation and variable selection method for partially linear models with large-dimensional covariates," Statistical Papers, Springer, vol. 61(5), pages 1911-1937, October.
    8. Elena McDonald & Xin Wang, 2024. "Generalized regression estimators with concave penalties and a comparison to lasso type estimators," METRON, Springer;Sapienza Università di Roma, vol. 82(2), pages 213-239, August.
    9. T. Cai & J. Huang & L. Tian, 2009. "Regularized Estimation for the Accelerated Failure Time Model," Biometrics, The International Biometric Society, vol. 65(2), pages 394-404, June.
    10. Z. John Daye & Jinbo Chen & Hongzhe Li, 2012. "High-Dimensional Heteroscedastic Regression with an Application to eQTL Data Analysis," Biometrics, The International Biometric Society, vol. 68(1), pages 316-326, March.
    11. Xiang Zhang & Yichao Wu & Lan Wang & Runze Li, 2016. "Variable selection for support vector machines in moderately high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 53-76, January.
    12. Wang, Hansheng & Leng, Chenlei, 2008. "A note on adaptive group lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5277-5286, August.
    13. Smucler, Ezequiel & Yohai, Victor J., 2017. "Robust and sparse estimators for linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 116-130.
    14. Long Feng & Changliang Zou & Zhaojun Wang & Xianwu Wei & Bin Chen, 2015. "Robust spline-based variable selection in varying coefficient model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(1), pages 85-118, January.
    15. Xiaofei Wu & Rongmei Liang & Hu Yang, 2022. "Penalized and constrained LAD estimation in fixed and high dimension," Statistical Papers, Springer, vol. 63(1), pages 53-95, February.
    16. Abdul Wahid & Dost Muhammad Khan & Ijaz Hussain, 2017. "Robust Adaptive Lasso method for parameter’s estimation and variable selection in high-dimensional sparse models," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-17, August.
    17. Bang, Sungwan & Jhun, Myoungshic, 2012. "Simultaneous estimation and factor selection in quantile regression via adaptive sup-norm regularization," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 813-826.
    18. Song, Yunquan & Liang, Xijun & Zhu, Yanji & Lin, Lu, 2021. "Robust variable selection with exponential squared loss for the spatial autoregressive model," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    19. Kean Ming Tan & Lan Wang & Wen‐Xin Zhou, 2022. "High‐dimensional quantile regression: Convolution smoothing and concave regularization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(1), pages 205-233, February.
    20. Jiang, Rong & Qian, Wei-Min, 2016. "Quantile regression for single-index-coefficient regression models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 305-317.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:249:y:2017:i:1:d:10.1007_s10479-016-2333-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.