On Lagrangian Twin Parametric-Margin Support Vector Machine

A new simple and linearly convergent scheme is proposed in this paper for the dual formulation of twin parametric-margin support vector machine. Here, instead of considering the 1-norm error of slack variables, we have considered 2-norm of the vector of slack variables to make the objective functions strongly convex. Further, the proposed method solves a pair of linearly convergent iterative schemes instead of solving a pair of quadratic programming problems as in case of twin support vector machine and twin parametric-margin support vector machine. The proposed method considers in finding two parametric-margin hyperplanes that makes it less sensitive to heteroscedastic noise structure. Our experiments, performed on synthetic and real-world datasets, conclude that the proposed method has comparable generalization performance and improved learning speed in comparison to twin support vector machine, Lagrangian twin support vector machine and twin parametric-margin support vector machine.

[1]  S. Balasundaram,et al.  A new approach for training Lagrangian twin support vector machine via unconstrained convex minimization , 2016, Applied Intelligence.

[2]  Madan Gopal,et al.  Application of smoothing technique on twin support vector machines , 2008, Pattern Recognit. Lett..

[3]  William M. Campbell,et al.  Support vector machines for speaker verification and identification , 2000, Neural Networks for Signal Processing X. Proceedings of the 2000 IEEE Signal Processing Society Workshop (Cat. No.00TH8501).

[4]  Brian D. Ripley,et al.  Pattern Recognition and Neural Networks , 1996 .

[5]  Muhammad Tanveer,et al.  Robust energy-based least squares twin support vector machines , 2015, Applied Intelligence.

[6]  Lan Bai,et al.  Twin Support Vector Machine for Clustering , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[7]  S. Balasundaram,et al.  Application of Lagrangian Twin Support Vector Machines for Classification , 2010, 2010 Second International Conference on Machine Learning and Computing.

[8]  Muhammad Tanveer,et al.  Newton method for implicit Lagrangian twin support vector machines , 2015, Int. J. Mach. Learn. Cybern..

[9]  Reshma Khemchandani,et al.  Robust least squares twin support vector machine for human activity recognition , 2016, Appl. Soft Comput..

[10]  Touradj Ebrahimi,et al.  Joint Time-Frequency-Space Classification of EEG in a Brain-Computer Interface Application , 2003, EURASIP J. Adv. Signal Process..

[11]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[12]  R. Chellappa.  Introduction of New Editor-in-Chief , 2005 .

[13]  Xinjun Peng,et al.  TPMSVM: A novel twin parametric-margin support vector machine for pattern recognition , 2011, Pattern Recognit..

[14]  S. Balasundaram,et al.  Lagrangian support vector regression via unconstrained convex minimization , 2014, Neural Networks.

[15]  Thorsten Joachims,et al.  Text Categorization with Support Vector Machines: Learning with Many Relevant Features , 1998, ECML.

[16]  Reshma Khemchandani,et al.  Twin Support Vector Machines for Pattern Classification , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Corinna Cortes,et al.  Support-Vector Networks , 1995, Machine Learning.

[18]  Olvi L. Mangasarian,et al.  Multisurface proximal support vector machine classification via generalized eigenvalues , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  Madan Gopal,et al.  Least squares twin support vector machines for pattern classification , 2009, Expert Syst. Appl..

[20]  Bernhard Schölkopf,et al.  New Support Vector Algorithms , 2000, Neural Computation.

[21]  Pei-Yi Hao,et al.  New support vector algorithms with parametric insensitive/margin model , 2010, Neural Networks.