By taking the sub-network as a kernel mapping from the original input space into a feature space, we present a novel model, called deep neural mapping support vector machine (DNMSVM), from the viewpoint of deep learning.
If the relationship between x i and y i is non-linear, SVR can perform non-linear regression by kernel tricks which implicitly map x i to higher-dimensional feature spaces, i.e., f (x) = 〈 w, Φ x)〉 + b, where Φ x) is a kernel mapping representation.
Since data is typically not linearly separable, it is mapped to a higher dimensional space by a kernel function.
This model is also a new and general kernel learning method, where the kernel mapping is indeed an explicit function expressed as a sub-network, different from an implicit function induced by a kernel function traditionally.
RKHS regression models use an implicit or explicit mapping of the input data into a high-dimensional feature space defined by a kernel function.
The sample x in the original space is first mapped into the kernel space by kernel mapping φ, then PCA is used to project φ(x) into P(φ(x)), which is a point in a PCA subspace.
The kernel mapping is a popular method for designing nonlinear process monitoring techniques.
In most cases, kernel mapping is achieved by using the radial basis kernel function which, in theory, is able to provide an infinite order nonlinear mapping.
This increases the class separation and is illustrated by way of an example, two opcodes pop and ret are used as they demonstrate the characteristics of kernel mapping.
We use a computationally efficient approximation of the non-linear kernel by Veldadi and Zisserman [50] which allows features to undergo a non-linear kernel map expansion before SVM classification.
