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Mathematical Problems in Engineering
Volume 2017, Article ID 4191789, 12 pages
Research Article

Reconstruct the Support Vectors to Improve LSSVM Sparseness for Mill Load Prediction

State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi’an Jiaotong University, Xi’an, China

Correspondence should be addressed to Jianquan Shi; moc.621@64nauqnaijihs

Received 24 October 2016; Revised 14 May 2017; Accepted 25 May 2017; Published 5 July 2017

Academic Editor: Erik Cuevas

Copyright © 2017 Gangquan Si 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 sparse strategy plays a significant role in the application of the least square support vector machine (LSSVM), to alleviate the condition that the solution of LSSVM is lacking sparseness and robustness. In this paper, a sparse method using reconstructed support vectors is proposed, which has also been successfully applied to mill load prediction. Different from other sparse algorithms, it no longer selects the support vectors from training data set according to the ranked contributions for optimization of LSSVM. Instead, the reconstructed data is obtained first based on the initial model with all training data. Then, select support vectors from reconstructed data set according to the location information of density clustering in training data set, and the process of selecting is terminated after traversing the total training data set. Finally, the training model could be built based on the optimal reconstructed support vectors and the hyperparameter tuned subsequently. What is more, the paper puts forward a supplemental algorithm to subtract the redundancy support vectors of previous model. Lots of experiments on synthetic data sets, benchmark data sets, and mill load data sets are carried out, and the results illustrate the effectiveness of the proposed sparse method for LSSVM.