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If the time-series is not linear, the regression model maps the time-series x to a higher dimension feature space by using kernel function φ(x).
This mapping is done by using kernel function such as polynomial or radial basis function kernel.
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The SVM model transforms the features into a higher dimension by using kernel functions to find an optimal separating hyperplane between two classes.
This mapping from the input vector space to the feature space is a nonlinear mapping achieved by using kernel functions.
Moreover, another technique adopted in our procedures to make the results stable is that the simulations are smoothed by using kernel functions.
The linear separability constraint which is certainly difficult to ensure in realistic situations, can be solved by using kernel functions to transform the input space to a higher dimensional RHKS [33].
It can classify highly nonlinear data using kernel function.
A commonly used kernel function is the Gaussian kernel given by: K (x i − x h ) = 1 (2 π ) p / 2 exp [ − 1 2 (x i − x h ) ′ (x i − x h ) ].
Widely used kernel function includes the triangle kernel, Gaussian kernel, Epanechnikov kernel among others.
We used an RBF (radial basis function) kernel in this study, as the RBF kernel is the most flexible and the most widely used kernel function.
Polynomial kernel and Gaussian kernel are commonly used kernel functions.
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