A weighted twin support vector regression

Twin support vector regression (TSVR) is a new regression algorithm, which aims at finding @e-insensitive up- and down-bound functions for the training points. In order to do so, one needs to resolve a pair of smaller-sized quadratic programming problems (QPPs) rather than a single large one in a classical SVR. However, the same penalties are given to the samples in TSVR. In fact, samples in the different positions have different effects on the bound function. Then, we propose a weighted TSVR in this paper, where samples in the different positions are proposed to give different penalties. The final regressor can avoid the over-fitting problem to a certain extent and yield great generalization ability. Numerical experiments on one artificial dataset and nine benchmark datasets demonstrate the feasibility and validity of our proposed algorithm.

[1]  Xinjun Peng,et al.  TSVR: An efficient Twin Support Vector Machine for regression , 2010, Neural Networks.

[2]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[3]  Yuanyuan Wang,et al.  A rough margin based support vector machine , 2008, Inf. Sci..

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

[5]  Xijin Tang,et al.  Text classification based on multi-word with support vector machine , 2008, Knowl. Based Syst..

[6]  Hao Wu,et al.  An effective feature selection method for hyperspectral image classification based on genetic algorithm and support vector machine , 2011, Knowl. Based Syst..

[7]  Xinjun Peng,et al.  A nu-twin support vector machine (nu-TSVM) classifier and its geometric algorithms , 2010, Inf. Sci..

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

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

[10]  Ching-Chiang Yeh,et al.  The use of hybrid manifold learning and support vector machines in the prediction of business failure , 2011, Knowl. Based Syst..

[11]  Yitian Xu,et al.  A rough margin-based linear ν support vector regression , 2012 .

[12]  M. Narasimha Murty,et al.  Rough support vector clustering , 2005, Pattern Recognit..

[13]  Reshma Khemchandani,et al.  Optimal kernel selection in twin support vector machines , 2009, Optim. Lett..

[14]  Ping Zhong,et al.  A rough margin-based ν-twin support vector machine , 2011, Neural Computing and Applications.

[15]  Glenn Fung,et al.  Multicategory Proximal Support Vector Machine Classifiers , 2005, Machine Learning.

[16]  Anirban Mukherjee,et al.  Nonparallel plane proximal classifier , 2009, Signal Process..

[17]  Reshma Khemchandani,et al.  Fuzzy multi-category proximal support vector classification via generalized eigenvalues , 2007, Soft Comput..

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