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Bounds for Sparse Solutions of K-SVCR Multi-class Classification Model

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Learning and Intelligent Optimization (LION 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13621))

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Abstract

The support vector classification-regression machine for k-class classification (K-SVCR) is a novel multi-class classification approach based on the “1-versus-1-versus-rest” structure. In this work, we suggested an efficient model by proposing the p-norm \((0<p< 1)\) instead of the 2-norm for the regularization term in the objective function of K-SVCR that can be used for feature selection. We derived lower bounds for the absolute value of nonzero entries in every local optimal solution of the p-norm based model. Also, we provided upper bounds for the number of nonzero components of the optimal solutions. We explored the link between solution sparsity, regularization parameters, and the p-choice.

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References

  1. Ahmad, A.S., et al.: A review on applications of ANN and SVM for building electrical energy consumption forecasting. Renew. Sustain. Energy Rev. 33, 102–109 (2014)

    Article  Google Scholar 

  2. Angulo, C., Català, A.: K-SVCR. a multi-class support vector machine. In: López de Mántaras, R., Plaza, E. (eds.) ECML 2000. LNCS (LNAI), vol. 1810, pp. 31–38. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-45164-1_4

    Chapter  Google Scholar 

  3. Arabasadi, Z., Alizadehsani, R., Roshanzamir, M., Moosaei, H., Yarifard, A.A.: Computer aided decision making for heart disease detection using hybrid neural network-genetic algorithm. Comput. Methods Programs Biomed. 141, 19–26 (2017)

    Article  Google Scholar 

  4. Bazikar, F., Ketabchi, S., Moosaei, H.: DC programming and DCA for parametric-margin \(\nu \)-support vector machine. Appl. Intell. 50(6), 1763–1774 (2020)

    Article  Google Scholar 

  5. Boser, B.E., Guyon, I.M., Vapnik, V.N.: A training algorithm for optimal margin classifiers. In: Haussler, D. (ed.) Proceedings of the Fifth Annual Workshop on Computational Learning Theory, pp. 144–152. COLT 1992, ACM, New York (1992)

    Google Scholar 

  6. Bottou, L., et al.: Comparison of classifier methods: a case study in handwritten digit recognition. In: Proceedings of the 12th IAPR International Conference on Pattern Recognition, Vol. 3-Conference C: Signal Processing (Cat. No. 94CH3440-5). vol. 2, pp. 77–82. IEEE (1994)

    Google Scholar 

  7. Bruckstein, A.M., Donoho, D.L., Elad, M.: From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Rev. 51(1), 34–81 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Chartrand, R.: Exact reconstruction of sparse signals via nonconvex minimization. IEEE Signal Process. Lett. 14(10), 707–710 (2007)

    Article  Google Scholar 

  9. Chartrand, R.: Nonconvex regularization for shape preservation. In: 2007 IEEE International Conference on Image Processing. vol. 1, pp. 293–297. IEEE (2007)

    Google Scholar 

  10. Cortes, C., Vapnik, V.: Support-vector networks. Mach. Learn. 20(3), 273–297 (1995)

    Article  MATH  Google Scholar 

  11. Déniz, O., Castrillon, M., Hernández, M.: Face recognition using independent component analysis and support vector machines. Pattern Recogn. Lett. 24(13), 2153–2157 (2003)

    Article  MATH  Google Scholar 

  12. Ding, S., Shi, S., Jia, W.: Research on fingerprint classification based on twin support vector machine. IET Image Proc. 14(2), 231–235 (2019)

    Article  Google Scholar 

  13. Ding, S., Zhang, N., Zhang, X., Wu, F.: Twin support vector machine: theory, algorithm and applications. Neural Comput. Appl. 28(11), 3119–3130 (2017)

    Article  Google Scholar 

  14. Fenn, M.B., Xanthopoulos, P., Pyrgiotakis, G., Grobmyer, S.R., Pardalos, P.M., Hench, L.L.: Raman spectroscopy for clinical oncology. Adv. Opt. Technol. 2011, 213783 (2011)

    Google Scholar 

  15. Ketabchi, S., Moosaei, H., Razzaghi, M., Pardalos, P.M.: An improvement on parametric \(\nu \) -support vector algorithm for classification. Ann. Oper. Res. 276(1–2), 155–168 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kreßel, U.H.G.: Pairwise Classification and Support Vector Machines, pp. 255–268. MIT Press, Cambridge (1999)

    Google Scholar 

  17. Li, G., Yang, L., Wu, Z., Wu, C.: DC programming for sparse proximal support vector machines. Inf. Sci. 547, 187–201 (2021)

    Article  MATH  Google Scholar 

  18. Ma, J., Zhou, S., Chen, L., Wang, W., Zhang, Z.: A sparse robust model for large scale multi-class classification based on K-SVCR. Pattern Recogn. Lett. 117, 16–23 (2019)

    Article  Google Scholar 

  19. Moosaei, H., Ketabchi, S., Razzaghi, M., Tanveer, M.: Generalized twin support vector machines. Neural Process. Lett. 53(2), 1–20 (2021)

    Google Scholar 

  20. Moosaei, H., Hladík, M.: Least squares approach to K-SVCR multi-class classification with its applications. Ann. Math. Artif. Intell. 90, 873–892 (2022). https://doi.org/10.1007/s10472-021-09747-1

    Article  MathSciNet  MATH  Google Scholar 

  21. Moosaei, H., Mousavi, A., Hladík, M., Gao, Z.: Sparse universum quadratic surface support vector machine models for binary classification. arXiv preprint arXiv:2104.01331 (2021)

  22. Pardalos, P.M., Boginski, V.L., Vazacopoulos, A.: Data Mining in Biomedicine, Springer Optimization and Its Applications, vol. 7. Springer (2007). https://doi.org/10.1007/978-0-387-69319-4

  23. Shao, M., Wang, X., Bu, Z., Chen, X., Wang, Y.: Prediction of energy consumption in hotel buildings via support vector machines. Sustain. Cities Soc. 57(6), 102128 (2020)

    Article  Google Scholar 

  24. Trafalis, T.B., Ince, H.: Support vector machine for regression and applications to financial forecasting. In: Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium. vol. 6, pp. 348–353. IEEE (2000)

    Google Scholar 

  25. Xu, Y., Guo, R., Wang, L.: A twin multi-class classification support vector machine. Cogn. Comput. 5(4), 580–588 (2013)

    Article  Google Scholar 

  26. Zhao, H.x., Magoulès, F.: A review on the prediction of building energy consumption. Renew. Sustain. Energy Rev. 16(6), 3586–3592 (2012)

    Google Scholar 

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Acknowledgments

The authors were supported by the Czech Science Foundation Grant P403-22-11117S. H. Moosaei was also supported by the Center for Foundations of Modern Computer Science (Charles Univ. project UNCE/SCI/004).

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Authors and Affiliations

  1. Department of Informatics, Faculty of Science, Jan Evangelista Purkyně University, Ústí nad Labem, Czech Republic

    Hossein Moosaei

  2. Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic

    Hossein Moosaei & Milan Hladík

Authors
  1. Hossein Moosaei
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  2. Milan Hladík
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Corresponding author

Correspondence to Hossein Moosaei .

Editor information

Editors and Affiliations

  1. SBA Research, Vienna, Austria

    Dimitris E. Simos

  2. Moscow Aviation Institute (National Research University), Moscow, Russia

    Varvara A. Rasskazova

  3. Università degli Studi di Milano-Bicocca, Milan, Italy

    Francesco Archetti

  4. Wilfrid Laurier University, Waterloo, ON, Canada

    Ilias S. Kotsireas

  5. University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

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Moosaei, H., Hladík, M. (2022). Bounds for Sparse Solutions of K-SVCR Multi-class Classification Model. In: Simos, D.E., Rasskazova, V.A., Archetti, F., Kotsireas, I.S., Pardalos, P.M. (eds) Learning and Intelligent Optimization. LION 2022. Lecture Notes in Computer Science, vol 13621. Springer, Cham. https://doi.org/10.1007/978-3-031-24866-5_11

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  • DOI: https://doi.org/10.1007/978-3-031-24866-5_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-24865-8

  • Online ISBN: 978-3-031-24866-5

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