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The Modified BAPGs Method for Support Vector Machine Classifier with Truncated Loss

DOI: 10.4236/am.2024.154015, PP. 267-278

Keywords: HTPSVM, Bregman Distance, BAPGs Algorithm

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Abstract:

In this paper, we modify the Bregman APGs (BAPGs) method proposed in (Wang, L, et al.) for solving the support vector machine problem with truncated loss (HTPSVM) given in (Zhu, W, et al.), we also add an adaptive parameter selection technique based on (Ren, K, et al.). In each iteration, we use the linear approximation method to get the explicit solution of the subproblem and set a function to apply the Bregman distance. Finally, numerical experiments are performed to verify the efficiency of BAPGs.

References

[1]  Vapnik, V. and Cortes, C. (1995) Support-Vector Networks. Machine Learning, 20, 273-297.
https://doi.org/10.1007/BF00994018
[2]  Joachims, T. (1998) Text Categorization with Support Vector Machines: Learning with Many Relevant Features. 10th European Conference on Machine Learning, Chemnitz, 21-23 April 1998, 137-142.
https://doi.org/10.1007/BFb0026683
[3]  Zhang, X., Li, A. and Pan, R. (2016) Stock Trend Prediction Based on a New Status Box Method and AdaBoost Probabilistic Support Vector Machine. Applied Soft Computing, 49, 385-398.
https://doi.org/10.1016/j.asoc.2016.08.026
[4]  Chandra, M. and Bedi, S. (2021) Survey on SVM and Their Application in Image Classification. International Journal of Information Technology, 13, 1-11.
https://doi.org/10.1007/s41870-017-0080-1
[5]  Rong-En, F., Kai-Wei, C., et al. (2008) LIBLINEAR: A Library for Large Linear Classification. The Journal of Machine Learning Research, 9, 1871-1874.
[6]  Suykens, J. and Vandewalle, J. (1999) Least Squares Support Vector Machine Classifiers. Neural Processing Letters, 9, 293-300.
https://doi.org/10.1023/A:1018628609742
[7]  Zhu, W., Song, Y. and Xiao, Y. (2021) Support Vector Machine Classifier with Huberized Pinball Loss. Engineering Applications of Artificial Intelligence, 91, Article 103635.
https://doi.org/10.1016/j.engappai.2020.103635
[8]  Zhao, L., Mammadov, M., et al. (2010) From Convex to Nonconvex: A Loss Function Analysis for Binary Classification. 2010 IEEE International Conference on Data Mining Workshops, Sydney, 13 December 2010, 1281-1288.
https://doi.org/10.1109/ICDMW.2010.57
[9]  Collobert, R., Sinz, F, et al. (2006) Large Scale Transductive SVMS. Journal of Machine Learning Research, 7, 1687-1712.
[10]  Shen, X., Niu, L., Qi, Z. and Tian, Y. (2017) Support Vector Machine Classifier with Truncated Pinball Loss. Pattern Recognition, 68, 199-210.
[11]  Zhu, W., Song, Y. and Xiao, Y. (2022) Robust Support Vector Machine Classifier with Truncated Loss Function by Gradient Algorithm. Computers & Industrial Engineering, 172, Article 108630.
[12]  Ren, K., Liu, C. and Wang, L. (2024) The Modified Second APG Method for a Class of Nonconvex Nonsmooth Problems. (In Press)
[13]  Lin, D. and Liu, C. (2019) The Modified Second APG Method for DC Optimization Problems. Optimization Letters, 13, 805-824.
https://doi.org/10.1007/s11590-018-1280-8
[14]  Wang, L., Liu, C. and Ren, K. (2024) The Bregman Modified Second APG Method for DC Optimization Problems. (In Press)
[15]  Rockafellar, R. and Wets, R. (2009) Variational Analysis. Springer Science & Business Media, Berlin.
[16]  Bolte, J., Sabach, S., Teboulle, M., et al. (2017) First Order Methods beyond Convexity and Lipschitz Gradient Continuity with Applications to Quadratic Inverse Problems. SIAM Journal on Optimization, 28, 2131-2151.
https://doi.org/10.1137/17M1138558
[17]  Lev, M.B. (1967) The Relaxation Method of Finding the Common Point of Convex Sets and Its Application to the Solution of Problems in Convex Programming. USSR Computational Mathematics and Mathematical Physics, 7, 200-217.
https://api.semanticscholar.org/corpusid:121309410
[18]  Wu, Z., Li, C., et al. (2021) Inertial Proximal Gradient Methods with Bregman Regularization for a Class of Nonconvex Optimization Problems. Journal of Global Optimization, 79, 617-644.
https://doi.org/10.1007/s10898-020-00943-7
[19]  Bauschke, H., Bolte, J. and Teboulle, M. (2017) A Descent Lemma beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications. Mathematics of Operations Research, 42, 330-348.
https://doi.org/10.1287/moor.2016.0817
[20]  Asuncion, A. and Newman, D. (2007) UCI Machine Learning Repository.
http://archive.ics.uci.edu/ml
[21]  Chen, X., Lu, Z., et al. (2016) Penalty Methods for a Class of Non-Lipschitz Optimization Problems. SIAM Journal on Optimization, 26, 1465-1492.
https://doi.org/10.1137/15M1028054

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