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Sparse representation based on projection method in online least squares support vector machines
Received:January 26,2007  Revised:May 16,2008
Keywords:Least squares support vector machines  Projection  Sparsity  pH neutralizing process  Isomerization
Fund Project:
Lijuan LI, Hongye SU , Jian CHU State Key Laboratory of Industrial Control Technology, Institute of Advanced Process Control, Zhejiang University, Hangzhou Zhejiang 310027, China; College of Automation, Nanjing University of Technology, Nanjing Jiangsu 210009, China 
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      A sparse approximation algorithm based on projection is presented in this paper in order to overcome the limitation of the non-sparsity of least squares support vector machines (LS-SVM). The new inputs are projected into the subspace spanned by previous basis vectors (BV) and those inputs whose squared distance from the subspace is higher than a threshold are added in the BV set, while others are rejected. This consequently results in the sparse approximation. In addition, a recursive approach to deleting an exiting vector in the BV set is proposed. Then the online LS-SVM, sparse approximation and BV removal are combined to produce the sparse online LS-SVM algorithm that can control the size of memory irrespective of the processed data size. The suggested algorithm is applied in the online modeling of a pH neutralizing process and the isomerization plant of a refinery, respectively. The detailed comparison of computing time and precision is also given between the suggested algorithm and the nonsparse one. The results show that the proposed algorithm greatly improves the sparsity just with little cost of precision.
Lijuan LI, Hongye SU , Jian CHU.Sparse representation based on projection method in online least squares support vector machines[J].Journal of Control Theory and Applications,2009,7(2):163~.
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