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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 5873769, 11 pages
http://dx.doi.org/10.1155/2016/5873769
Research Article

Efficient Optimization of -Measure with Cost-Sensitive SVM

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 15 December 2015; Revised 2 March 2016; Accepted 22 March 2016

Academic Editor: Hiroyuki Mino

Copyright © 2016 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.

Abstract

-measure is one of the most commonly used performance metrics in classification, particularly when the classes are highly imbalanced. Direct optimization of this measure is often challenging, since no closed form solution exists. Current algorithms design the classifiers by using the approximations to the -measure. These algorithms are not efficient and do not scale well to the large datasets. To fill the gap, in this paper, we propose a novel algorithm, which can efficiently optimize -measure with cost-sensitive SVM. First of all, we present an explicit transformation from the optimization of -measure to cost-sensitive SVM. Then we adopt bundle method to solve the inner optimization. For the problem where the existing bundle method may have the fluctuations in the primal objective during iterations, an additional line search procedure is involved, which can alleviate the fluctuations problem and make our algorithm more efficient. Empirical studies on the large-scale datasets demonstrate that our algorithm can provide significant speedups over current state-of-the-art -measure based learners, while obtaining better (or comparable) precise solutions.