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Abstract and Applied Analysis
Volume 2014, Article ID 197476, 8 pages
Research Article

Convergence Analysis of an Empirical Eigenfunction-Based Ranking Algorithm with Truncated Sparsity

1School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
2College of Information, Dalian University, Dalian 116622, China
3Beijing Key Laboratory of Multimedia Intelligent Software Technology, College of Metropolitan Transportation, Beijing University of Technology, Beijing 100124, China

Received 13 April 2014; Revised 8 July 2014; Accepted 9 July 2014; Published 21 July 2014

Academic Editor: Sergei V. Pereverzyev

Copyright © 2014 Min Xu 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.


We study an empirical eigenfunction-based algorithm for ranking with a data dependent hypothesis space. The space is spanned by certain empirical eigenfunctions which we select by using a truncated parameter. We establish the representer theorem and convergence analysis of the algorithm. In particular, we show that under a mild condition, the algorithm produces a satisfactory convergence rate as well as sparse representations with respect to the empirical eigenfunctions.