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Functional-bandwidth kernel for Support Vector Machine with Functional Data: An alternating optimization algorithm

Author

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  • Blanquero, R.
  • Carrizosa, E.
  • Jiménez-Cordero, A.
  • Martín-Barragán, B.

Abstract

Functional Data Analysis (FDA) is devoted to the study of data which are functions. Support Vector Machine (SVM) is a benchmark tool for classification, in particular, of functional data. SVM is frequently used with a kernel (e.g.: Gaussian) which involves a scalar bandwidth parameter. In this paper, we propose to use kernels with functional bandwidths. In this way, accuracy may be improved, and the time intervals critical for classification are identified. Tuning the functional parameters of the new kernel is a challenging task expressed as a continuous optimization problem, solved by means of a heuristic. Our experiments with benchmark data sets show the advantages of using functional parameters and the effectiveness of our approach.

Suggested Citation

  • Blanquero, R. & Carrizosa, E. & Jiménez-Cordero, A. & Martín-Barragán, B., 2019. "Functional-bandwidth kernel for Support Vector Machine with Functional Data: An alternating optimization algorithm," European Journal of Operational Research, Elsevier, vol. 275(1), pages 195-207.
    • Handle: RePEc:eee:ejores:v:275:y:2019:i:1:p:195-207
    DOI: 10.1016/j.ejor.2018.11.024
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    1. Febrero-Bande, Manuel & de la Fuente, Manuel Oviedo, 2012. "Statistical Computing in Functional Data Analysis: The R Package fda.usc," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i04).
    2. Maldonado, Sebastián & Pérez, Juan & Bravo, Cristián, 2017. "Cost-based feature selection for Support Vector Machines: An application in credit scoring," European Journal of Operational Research, Elsevier, vol. 261(2), pages 656-665.
    3. Laukaitis, Algirdas & Rackauskas, Alfredas, 2005. "Functional data analysis for clients segmentation tasks," European Journal of Operational Research, Elsevier, vol. 163(1), pages 210-216, May.
    4. López-Pintado, Sara & Romo, Juan, 2009. "On the Concept of Depth for Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 718-734.
    5. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2006. "On the use of the bootstrap for estimating functions with functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1063-1074, November.
    6. J. Paul Brooks, 2011. "Support Vector Machines with the Ramp Loss and the Hard Margin Loss," Operations Research, INFORMS, vol. 59(2), pages 467-479, April.
    7. Antonio Cuevas & Manuel Febrero & Ricardo Fraiman, 2007. "Robust estimation and classification for functional data via projection-based depth notions," Computational Statistics, Springer, vol. 22(3), pages 481-496, September.
    8. Lessmann, Stefan & Voß, Stefan, 2009. "A reference model for customer-centric data mining with support vector machines," European Journal of Operational Research, Elsevier, vol. 199(2), pages 520-530, December.
    9. Martin-Barragan, Belen & Lillo, Rosa & Romo, Juan, 2014. "Interpretable support vector machines for functional data," European Journal of Operational Research, Elsevier, vol. 232(1), pages 146-155.
    10. Wang, Haifeng & Zheng, Bichen & Yoon, Sang Won & Ko, Hoo Sang, 2018. "A support vector machine-based ensemble algorithm for breast cancer diagnosis," European Journal of Operational Research, Elsevier, vol. 267(2), pages 687-699.
    11. Aurore Delaigle & Peter Hall, 2012. "Achieving near perfect classification for functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(2), pages 267-286, March.
    12. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    13. Ashish Sood & Gareth M. James & Gerard J. Tellis, 2009. "Functional Regression: A New Model for Predicting Market Penetration of New Products," Marketing Science, INFORMS, vol. 28(1), pages 36-51, 01-02.
    14. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    15. Raul Cruz-Cano & David S. H. Chew & Kwok-Pui Choi & Ming-Ying Leung, 2010. "Least-Squares Support Vector Machine Approach to Viral Replication Origin Prediction," INFORMS Journal on Computing, INFORMS, vol. 22(3), pages 457-470, August.
    16. Amparo Baíllo & Antonio Cuevas & Juan Antonio Cuesta‐Albertos, 2011. "Supervised Classification for a Family of Gaussian Functional Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(3), pages 480-498, September.
    17. Sain, Stephan R., 2002. "Multivariate locally adaptive density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 39(2), pages 165-186, April.
    18. Duong, Tarn & Cowling, Arianna & Koch, Inge & Wand, M.P., 2008. "Feature significance for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4225-4242, May.
    19. Cristian Preda & Gilbert Saporta & Caroline Lévéder, 2007. "PLS classification of functional data," Computational Statistics, Springer, vol. 22(2), pages 223-235, July.
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    2. Emilio Carrizosa & Cristina Molero-Río & Dolores Romero Morales, 2021. "Mathematical optimization in classification and regression trees," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 5-33, April.
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    5. Gao, Zheming & Fang, Shu-Cherng & Luo, Jian & Medhin, Negash, 2021. "A kernel-free double well potential support vector machine with applications," European Journal of Operational Research, Elsevier, vol. 290(1), pages 248-262.

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