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A Note on the Decomposition Methods for Support Vector Regression

b6506060{at}csie.ntu.edu.tx, Department of Computer Science and Information Engineering, National Taiwan University, Taipei 106, Taiwan

Hsuan-Tien Lin

b6506054{at}csie.ntu.edu.tw, Department of Computer Science and Information Engineering, National Taiwan University, Taipei 106, Taiwan

Chih-Jen Lin

cjlin{at}csie.ntu.edu.tw, Department of Computer Science and Information Engineering, National Taiwan University, Taipei 106, Taiwan

The dual formulation of support vector regression involves two closely related sets of variables. When the decomposition method is used, many existing approaches use pairs of indices from these two sets as the working set. Basically, they select a base set first and then expand it so all indices are pairs. This makes the implementation different from that for support vector classification. In addition, a larger optimization subproblem has to be solved in each iteration. We provide theoretical proofs and conduct experiments to show that using the base set as the working set leads to similar convergence (number of iterations). Therefore, by using a smaller working set while keeping a similar number of iterations, the program can be simpler and more efficient.