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Mathematical Problems in Engineering
Volume 2015, Article ID 294985, 7 pages
Research Article

Support Vector Machines for Unbalanced Multicategory Classification

Department of Statistics and Computer Science, Kunsan National University, Gunsan 573-701, Republic of Korea

Received 16 December 2014; Revised 6 February 2015; Accepted 7 February 2015

Academic Editor: Yaguo Lei

Copyright © 2015 Kang-Mo Jung. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Classification is a very important research topic and its applications are various, because data can be easily obtained in these days. Among many techniques of classification the support vector machine (SVM) is widely applied to bioinformatics or genetic analysis, because it gives sound theoretical background and its performance is superior to other methods. The SVM can be rewritten by a combination of the hinge loss function and the penalty function. The smoothly clipped absolute deviation penalty function satisfies desirably statistical properties. Since standard SVM techniques typically treat all classes equally, it is not well suited to unbalanced proportion data. We propose a robust method to treat unbalanced cases based on the weights of the class. Simulation and a numerical example show that the proposed method is effective to analyze unbalanced proportion data.