Abstract
The support vector machine (SVM) is a popular learning method for binary classification. Standard SVMs treat all the data points equally, but in some practical problems it is more natural to assign different weights to observations from different classes. This leads to a broader class of learning, the socalled weighted SVMs (WSVMs), and one of their important applications is to estimate class probabilities besides learning the classification boundary. There are two parameters associated with theWSVM optimization problem: one is the regularization parameter and the other is the weight parameter. In this article, we first establish that the WSVM solutions are jointly piecewiselinear with respect to both the regularization and weight parameter.We then develop a stateoftheart algorithm that can compute the entire trajectory of the WSVM solutions for every pair of the regularization parameter and the weight parameter at a feasible computational cost. The derived twodimensional solution surface provides theoretical insight on the behavior of the WSVM solutions. Numerically, the algorithm can greatly facilitate the implementation of the WSVM and automate the selection process of the optimal regularization parameter. We illustrate the new algorithm on various examples. This article has online supplementary materials.
Original language  English (US) 

Pages (fromto)  383402 
Number of pages  20 
Journal  Journal of Computational and Graphical Statistics 
Volume  23 
Issue number  2 
DOIs  
State  Published  2014 
Keywords
 Binary classification
 Coefficient path algorithm
 Probability estimation
 SVM
ASJC Scopus subject areas
 Statistics and Probability
 Discrete Mathematics and Combinatorics
 Statistics, Probability and Uncertainty
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TwoDimensional Solution Surface for Weighted Support Vector Machines
Shin, S. J. (Creator), Wu, Y. (Contributor) & Zhang, H. (Creator), Taylor & Francis, 2014
DOI: 10.6084/m9.figshare.1008435.v1, https://tandf.figshare.com/articles/dataset/Two_Dimensional_Solution_Surface_for_Weighted_Support_Vector_Machines/1008435/1
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