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Mathematical Problems in Engineering
Volume 2013, Article ID 602341, 10 pages
Research Article

A Novel Sparse Least Squares Support Vector Machines

1School of Mechanical and Electrical Engineering, Jiaxing University, Jiaxing 314001, China
2School of Engineering, Zhejiang Normal University, Jinhua 321004, China
3School of Electronics, Electrical Engineering and Computer Science, Queen's University of Belfast, Belfast BT9 5AH, UK

Received 9 August 2012; Accepted 6 December 2012

Academic Editor: Huaguang Zhang

Copyright © 2013 Xiao-Lei Xia 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.


The solution of a Least Squares Support Vector Machine (LS-SVM) suffers from the problem of nonsparseness. The Forward Least Squares Approximation (FLSA) is a greedy approximation algorithm with a least-squares loss function. This paper proposes a new Support Vector Machine for which the FLSA is the training algorithm—the Forward Least Squares Approximation SVM (FLSA-SVM). A major novelty of this new FLSA-SVM is that the number of support vectors is the regularization parameter for tuning the tradeoff between the generalization ability and the training cost. The FLSA-SVMs can also detect the linear dependencies in vectors of the input Gramian matrix. These attributes together contribute to its extreme sparseness. Experiments on benchmark datasets are presented which show that, compared to various SVM algorithms, the FLSA-SVM is extremely compact, while maintaining a competitive generalization ability.