Knowledge based proximal support vector machines

We propose a proximal version of the knowledge based support vector machine formulation, termed as knowledge based proximal support vector machines (KBPSVMs) in the sequel, for binary data classification. The KBPSVM classifier incorporates prior knowledge in the form of multiple polyhedral sets, and determines two parallel planes that are kept as distant from each other as possible. The proposed algorithm is simple and fast as no quadratic programming solver needs to be employed. Effectively, only the solution of a structured system of linear equations is needed.

[1]  David R. Musicant,et al.  Lagrangian Support Vector Machines , 2001, J. Mach. Learn. Res..

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

[3]  David R. Musicant,et al.  Active Support Vector Machine Classification , 2000, NIPS.

[4]  S. Gunn.  Support Vector Machines for Classification and Regression , 1998 .

[5]  Gene H. Golub,et al.  Matrix computations , 1983 .

[6]  Glenn Fung,et al.  Knowledge-Based Support Vector Machine Classifiers , 2002, NIPS.

[7]  Alexander J. Smola,et al.  Advances in Large Margin Classifiers , 2000 .

[8]  Olvi L. Mangasarian,et al.  Nonlinear Programming , 1969 .

[9]  Christopher J. C. Burges,et al.  A Tutorial on Support Vector Machines for Pattern Recognition , 1998, Data Mining and Knowledge Discovery.

[10]  John T. Ormerod,et al.  Knowledge-based semidefinite linear programming classifiers , 2006, Optim. Methods Softw..

[11]  Yuh-Jye Lee,et al.  Survival-Time Classification of Breast Cancer Patients , 2003, Comput. Optim. Appl..

[12]  David G. Stork,et al.  Pattern Classification , 1973 .

[13]  Olvi L. Mangasarian,et al.  Generalized Support Vector Machines , 1998 .

[14]  Vladimir Cherkassky,et al.  Learning from Data: Concepts, Theory, and Methods , 1998 .

[15]  Paul S. Bradley,et al.  Feature Selection via Concave Minimization and Support Vector Machines , 1998, ICML.

[16]  Glenn Fung,et al.  Proximal support vector machine classifiers , 2001, KDD '01.

[17]  Olvi L. Mangasarian,et al.  Nonlinear Knowledge-Based Classification , 2008, IEEE Transactions on Neural Networks.