Abstract
In this paper, we propose a novel feature selection method which can suppress the input features automatically. We first introduce a Tikhonov regularization term to the objective function of projection twin support vector machine (PTSVM). Then we convert it to a linear programming (LP) problem by replacing all the 2-norm terms in the objective function with 1-norm ones. Then we construct an unconstrained convex programming problem according to the exterior penalty (EP) theory. Finally, we solve the EP problems by using a fast generalized Newton algorithm. In order to improve performance, we apply a recursive algorithm to generate multiple projection axes for each class. To disclose the feasibility and effectiveness of our method, we conduct some experiments on UCI and Binary Alphadigits data sets.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Bradley, S., Mangasarian, O.L.: Massive data discrimination via linear support vector machines. Optim. Methods Softw. 13, 1–10 (2000)
Fung, G.M., Mangasarian, O.L.: Multicategory proximal support vector machine classifiers. Mach. Learn. 59(1–2), 77–97 (2005)
Mangasarian, O.L., Wild, E.: MultisurFace proximal support vector machine classification via generalized eigenvalues. IEEE Trans. Pattern Anal. Mach. Intell. 28(1), 69–74 (2006)
Jayadeva, Khemchandani, R., Chandra, S.: Twin support vector machines for pattern classification. IEEE Trans. Pattern Anal. Mach. Intell. 29(5), 905–910 (2007)
Ye, Q., Zhao, C., Ye, N., et al.: Multi-weight vector projection support vector machines. Pattern Recogn. Lett. 42(13), 2006–2011 (2010)
Chen, X., Yang, J., Ye, Q., et al.: Recursive projection twin support vector machine via within-class variance minimization. Pattern Recogn. 44(10–11), 2643–2655 (2011)
Tikhonov, A.N., Arsenin, V.Y.: Solutions of Ill-posed Problems. Translated from the Russian, Preface by translation John, F. (ed.), Scripta Series in Mathematics (1977)
Fung, G., Mangasarian, O.L.: A feature selection Newton method for support vector machine classification. Comput. Optim. Appl. 28(2), 185–202 (2004)
Mangasarian, O.L.: Exact 1-norm support vector machines via unconstrained convex differentiable minimization. J. Mach. Learn. Res. 7, 1517–1530 (2006)
Mangasarian, O.L.: A finite Newton method for classification problems. Optim. Methods Softw. 17, 913–929 (2002)
Qi, Z., Tian, Y., Shi, Y.: Structural twin support vector machine for classification. Knowl. Based Syst. 43, 74–81 (2013)
Chen, W.J., Shao, Y.H., Li, C.N., et al.: MLTSVM: a novel twin support vector machine to multi-label learning. Pattern Recogn. 52, 61–74 (2016)
Shao, Y.H., Wang, Z., Chen, W.J., et al.: A regularization for the projection twin support vector machine. Knowl. Based Syst. 37, 203–210 (2013)
Guo, J., Yi, P., Wang, R., et al.: Feature selection for least squares projection twin support vector machine. Neurocomputing 144, 174–183 (2014)
Gao, S., Ye, Q., Ye, N.: 1-Norm least squares twin support vector machines. Neurocomputing 74(17), 3590–3597 (2011)
Ye, Q., Zhao, C., Ye, N., et al.: A feature selection method for nonparallel plane support vector machine classification. Optim. Methods Softw. 27(3), 431–443 (2012)
Acknowledgement
This work was supported in part by the National Foundation for Distinguished Young Scientists under Grant 31125008, in part by the Scientific Research Foundation for Advanced Talents and Returned Overseas Scholars of Nanjing Forestry University, in part by the Natural Science Foundation of the Jiangsu Higher Education Institutions, China, under Grant 14KJB520018, in part by the Practice Innovation Training Program Projects for Jiangsu College Students under Grant 2015sjcx119, and in part by the National Science Foundation of China under Grant 61101197 and Grant 61401214.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Yan, R., Ye, Q., Zhang, D., Ye, N., Li, X. (2016). 1-Norm Projection Twin Support Vector Machine. In: Tan, T., Li, X., Chen, X., Zhou, J., Yang, J., Cheng, H. (eds) Pattern Recognition. CCPR 2016. Communications in Computer and Information Science, vol 662. Springer, Singapore. https://doi.org/10.1007/978-981-10-3002-4_44
Download citation
DOI: https://doi.org/10.1007/978-981-10-3002-4_44
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-3001-7
Online ISBN: 978-981-10-3002-4
eBook Packages: Computer ScienceComputer Science (R0)