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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 269856, 10 pages
Research Article

A Structural SVM Based Approach for Binary Classification under Class Imbalance

1Key Laboratory of Intelligent Computing & Signal Processing, Ministry of Education, Anhui University, No. 3, Feixi Road, Hefei, Anhui 230039, China
2School of Computer, Anhui University, No. 3, Feixi Road, Hefei 230039, China

Received 4 January 2015; Accepted 4 May 2015

Academic Editor: Haibo He

Copyright © 2015 Fan Cheng et al. 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.


Class imbalance situations, where one class is rare compared to the other, arise frequently in machine learning applications. It is well known that the usual misclassification error is not suitable in such settings. A wide range of performance measures such as AM and QM have been proposed for this problem. However, due to computational difficulties, few learning techniques have been developed to directly optimize for AM or QM metric. To fill the gap, in this paper, we present a general structural SVM framework for directly optimizing AM and QM. We define the loss functions oriented to AM and QM, respectively, and adopt the cutting plane algorithm to solve the outer optimization. For the inner problem of finding the most violated constraint, we propose two efficient algorithms for the AM and QM problem. Empirical studies on the various imbalanced datasets justify the effectiveness of the proposed approach.