For higher order polynomial kernels, the resulting mapping results in a highly dimensional feature space, but for lower order kernels (degree 2 and possibly 3), explicit calculation is feasible.
The Table 2 presents results with polynomial kernel with degrees 3, 5, 7, 9, 11 and 13.
For polynomial kernel, three degrees such as 2 (named as SVM polynomial2), 3 (named as SVM polynomial3), and 4 (named as SVM polynomial4) are tested.
Being aware that in several application domains, SVM have been shown to outperform competing techniques by using nonlinear kernels, which implicitly map the instances to very high (even infinite) dimensional spaces, we used polynomials kernels with degrees 1, 2, and 3. Multilayered Perceptron is a feed-forward artificial neural network model [ 37].
Xin and Yang in [3] proved Hilbert-type inequalities with the homogeneous kernel of degree −2.
Noticing that inequality (1.1) is a Homogenous kernel of degree −1, in 2009, a survey of the study of Hilbert-type inequalities with the homogeneous kernels of degree negative numbers and some parameters is given by [4].
Noticing that inequality (1) is a homogeneous kernel of degree −1, in 2009, A survey of the study of Hilbert-type inequalities with the homogeneous kernels of degree negative numbers and some parameters is given by [4].
For the homogeneous kernel of degree −1, Yang [129] considered some sufficient conditions to obtain (|T|=k_{0}(p)).
In this paper, we introduce a more general homogeneous kernel whose degree is given by two parameters (Definition 2.3).
