Journal of Applied Mathematics
Volume 2012 (2012), Article ID 189753, 13 pages
http://dx.doi.org/10.1155/2012/189753
Research Article

Approximation Analysis of Gradient Descent Algorithm for Bipartite Ranking

Hong Chen,1 Fangchao He,2,3 and Zhibin Pan1

1College of Science, Huazhong Agricultural University, Wuhan 430070, China
2School of Science, Hubei University of Technology, Wuhan 430068, China
3Faculty of Mathematics and Computer Science, Hubei University, Wuhan 430062, China

Received 9 March 2012; Revised 12 May 2012; Accepted 26 May 2012

Academic Editor: Yuesheng Xu

Copyright © 2012 Hong Chen 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

We introduce a gradient descent algorithm for bipartite ranking with general convex losses. The implementation of this algorithm is simple, and its generalization performance is investigated. Explicit learning rates are presented in terms of the suitable choices of the regularization parameter and the step size. The result fills the theoretical gap in learning rates for ranking problem with general convex losses.