Various wavelet basis functions were selected in wavelet applications.
This 17 basis functions could be compared to the result for a multicarrier equalizer in [4], where at least 30 basis functions were selected by using a different approach that resorts to enumerating the contribution at certain frequencies.
The optimal subset of the basis function is selected with the global optimization algorithm; which can accurately represent the trend of true response surface.
In the SVM model, a Gaussian radial basis function was selected as the kernel function with an error penalty factor (C = 1) and a scaling factor (σ = 0.01).
A radial basis function is selected as kernel for this binary classifier and parameter tuning is implemented with a 5-fold cross-validation loop on the training data (Van Landeghem et al., 2010).
The total number of tested basis functions is 1,458 when considering symmetric representation of Equation 5, from which only 17 basis functions are finally selected and reported in Table 2. Thus, 17 basis functions are used in the mitigation technique, which is formed as a linear combination of the basis indicated in Table 2.
As the kernels, four kinds of kernel functions, radial basis function (RBF), polynomial function, linear function, and sigmoid function, were selected to implement the experiment.
Online multiscale basis functions are constructed adaptively in some selected regions based on our error indicators.
In future work, we plan to relax the condition that radial basis function centres are selected form a pre-defined grid in order to reach the optimal number of degrees of freedom in the approximation and extend the algorithm to high-dimensional cases.
Multiscale basis functions are constructed using eigenvectors of a carefully selected local spectral problem.
