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Top2. Methodology
The support vector machine (SVM) first proposed by Cortes & Vapnik is gaining popularity because of its excellent properties of high generalization performance and global optimal solution (Cortes & Vapnik, 1995). Not only its structure is simple, but also its various technical capabilities is obviously boosted, especially the generalization ability. The detailed explanation and proof of SVM may be contained in the book (Ukil, 2007).
For given training set:
,
,
First, through nonlinear transform of 
,the paper mapped the input space into Hilbert space (Qin, S. J., & Badgwell, T. A., 2003), to construct the optimal linear function:
(1)Thus, it could get the linear approximation in feature space, Vapnik advanced that could take 
-insensitive loss function as measurement of approximation:
(2)