American Institute of Mathematical Sciences

Advanced
July  2007, 3(3): 529-542. doi: 10.3934/jimo.2007.3.529

Spline function smooth support vector machine for classification

Yubo Yuan 1, , Weiguo Fan 2, and  Dongmei Pu 1,

1. 

School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, 610054, China, China
2. 

Accounting & Information Systems, Virginia Polytechnic Institute and State University, VA, 24061, United States

Received  September 2006 Revised  May 2007 Published  July 2007

Support vector machine (SVM) is a very popular method for binary data classification in data mining (machine learning). Since the objective function of the unconstrained SVM model is a non-smooth function, a lot of good optimal algorithms can't be used to find the solution. In order to overcome this model's non-smooth property, Lee and Mangasarian proposed smooth support vector machine (SSVM) in 2001. Later, Yuan et al. proposed the polynomial smooth support vector machine (PSSVM) in 2005. In this paper, a three-order spline function is used to smooth the objective function and a three-order spline smooth support vector machine model (TSSVM) is obtained. By analyzing the performance of the smooth function, the smooth precision has been improved obviously. Moreover, BFGS and Newton-Armijo algorithms are used to solve the TSSVM model. Our experimental results prove that the TSSVM model has better classification performance than other competitive baselines.
Keywords: Support Vector Machine., Quadratic Programming, Data Mining.
Mathematics Subject Classification: Primary: 90C20; Secondary: 65L07; 65N1.
Citation: Yubo Yuan, Weiguo Fan, Dongmei Pu. Spline function smooth support vector machine for classification. Journal of Industrial and Management Optimization, 2007, 3 (3) : 529-542. doi: 10.3934/jimo.2007.3.529
[1]

Jian Luo, Shu-Cherng Fang, Yanqin Bai, Zhibin Deng. Fuzzy quadratic surface support vector machine based on fisher discriminant analysis. Journal of Industrial and Management Optimization, 2016, 12 (1) : 357-373. doi: 10.3934/jimo.2016.12.357
[2]

Ahmad Mousavi, Zheming Gao, Lanshan Han, Alvin Lim. Quadratic surface support vector machine with L1 norm regularization. Journal of Industrial and Management Optimization, 2022, 18 (3) : 1835-1861. doi: 10.3934/jimo.2021046
[3]

Qianru Zhai, Ye Tian, Jingyue Zhou. A SMOTE-based quadratic surface support vector machine for imbalanced classification with mislabeled information. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2021230
[4]

Yubo Yuan. Canonical duality solution for alternating support vector machine. Journal of Industrial and Management Optimization, 2012, 8 (3) : 611-621. doi: 10.3934/jimo.2012.8.611
[5]

Ying Lin, Qi Ye. Support vector machine classifiers by non-Euclidean margins. Mathematical Foundations of Computing, 2020, 3 (4) : 279-300. doi: 10.3934/mfc.2020018
[6]

Xin Li, Ziguan Cui, Linhui Sun, Guanming Lu, Debnath Narayan. Research on iterative repair algorithm of Hyperchaotic image based on support vector machine. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1199-1218. doi: 10.3934/dcdss.2019083
[7]

Xin Yan, Hongmiao Zhu. A kernel-free fuzzy support vector machine with Universum. Journal of Industrial and Management Optimization, 2023, 19 (1) : 282-299. doi: 10.3934/jimo.2021184
[8]

Fatemeh Bazikar, Saeed Ketabchi, Hossein Moosaei. Smooth augmented Lagrangian method for twin bounded support vector machine. Numerical Algebra, Control and Optimization, 2022, 12 (4) : 659-678. doi: 10.3934/naco.2021027
[9]

Ning Lu, Ying Liu. Application of support vector machine model in wind power prediction based on particle swarm optimization. Discrete and Continuous Dynamical Systems - S, 2015, 8 (6) : 1267-1276. doi: 10.3934/dcdss.2015.8.1267
[10]

Huiqin Zhang, JinChun Wang, Meng Wang, Xudong Chen. Integration of cuckoo search and fuzzy support vector machine for intelligent diagnosis of production process quality. Journal of Industrial and Management Optimization, 2022, 18 (1) : 195-217. doi: 10.3934/jimo.2020150
[11]

Ye Tian, Wei Yang, Gene Lai, Menghan Zhao. Predicting non-life insurer's insolvency using non-kernel fuzzy quadratic surface support vector machines. Journal of Industrial and Management Optimization, 2019, 15 (2) : 985-999. doi: 10.3934/jimo.2018081
[12]

K. Schittkowski. Optimal parameter selection in support vector machines. Journal of Industrial and Management Optimization, 2005, 1 (4) : 465-476. doi: 10.3934/jimo.2005.1.465
[13]

Pooja Louhan, S. K. Suneja. On fractional vector optimization over cones with support functions. Journal of Industrial and Management Optimization, 2017, 13 (2) : 549-572. doi: 10.3934/jimo.2016031
[14]

Florian Dumpert. Quantitative robustness of localized support vector machines. Communications on Pure and Applied Analysis, 2020, 19 (8) : 3947-3956. doi: 10.3934/cpaa.2020174
[15]

Hong-Gunn Chew, Cheng-Chew Lim. On regularisation parameter transformation of support vector machines. Journal of Industrial and Management Optimization, 2009, 5 (2) : 403-415. doi: 10.3934/jimo.2009.5.403
[16]

Henry Adams, Elin Farnell, Brittany Story. Support vector machines and Radon's theorem. Foundations of Data Science, 2022  doi: 10.3934/fods.2022017
[17]

Qinglei Zhang, Wenying Feng. Detecting coalition attacks in online advertising: A hybrid data mining approach. Big Data & Information Analytics, 2016, 1 (2&3) : 227-245. doi: 10.3934/bdia.2016006
[18]

Zhen Mei. Manifold data mining helps businesses grow more effectively. Big Data & Information Analytics, 2016, 1 (2&3) : 275-276. doi: 10.3934/bdia.2016009
[19]

Sunmoo Yoon, Maria Patrao, Debbie Schauer, Jose Gutierrez. Prediction models for burden of caregivers applying data mining techniques. Big Data & Information Analytics, 2017  doi: 10.3934/bdia.2017014
[20]

Anupama N, Sudarson Jena. A novel approach using incremental under sampling for data stream mining. Big Data & Information Analytics, 2018  doi: 10.3934/bdia.2017017

2021 Impact Factor: 1.411

Tools

Metrics

  • PDF downloads (176)
  • HTML views (0)
  • Cited by (16)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy