2 Methodology
The proposed SVATARK downscaling method mainly consists of both trend
and residual models. In this section, we briefly describe the
downscaling model components SVR and ATAK and the experimental
downscaling scheme.
2.1 Support vector regression method
Support vector machines (SVMs) have been widely applied to
classification and regression, which minimize both empirical risk and
structural risk to seek the best compromise between the complexity and
learning capability of a model (Srivastava et al., 2013; Sujay and Deka,
2014). For regression, SVR was first introduced by Vapnik et al. (1997).
Let \(\chi=\{x_{i},y_{i};i=1,\cdots,n\}\) be the training dataset
with ancillary vectors \(x_{i}\) and corresponding targets \(y_{i}\).
The input space \(\chi\) can be mapped into some feature space \(\Phi\)using the nonlinear function \(\varphi=\chi\rightarrow\Phi\). In the
feature space \(\Phi\), the training data may exhibit linearity, which
can be approximated by linear regression. The general form of the
nonlinear SVR function can be expressed as: