Combination of two kernel functions

Question

Could you help me with this kernel function?

\begin{equation} K(x,y) = (x \cdot y)^{2} + (x \cdot y), \text{ where } x = (x_1, x_2)', y = (y_1, y_2)' \end{equation}

I want to know if the combination of two kernel functions is still a kernel function and what is the result of this kernel function?

Given that $x$ and $y$ are vectors, what does the notation $xy$ indicate? Do you mean the dot product? The site supports mathjax/latex; please use this to format equations. — user20160, Apr 26 '20 at 17:01

score 1 · Answer 1 · answered Apr 26 '20 at 18:39

In your specific example, since the summand terms (i.e. the polynomial and the linear kernels respectively) are valid kernels, their sum is another kernel as well. The general case for linear combinations of kernels is proved in another beautiful post.

Combination of two kernel functions

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