Inner Product Kernel $k(x,y) = (1+\epsilon)^{\langle x, y \rangle}$

Question

Where in the literature is the inner product kernel $k(x,y) = (1+\epsilon)^{\langle x, y \rangle}$ mentioned? Does it have a name?

Answer 1

I wonder where you saw it. I do not know the answer. But I would like to mention that it is related an exponential kernel

$k_e(x,y) = \exp(\langle x,y \rangle).$

Assume $\epsilon>0$. Then

$k(x, y) = (1+\epsilon)^{\langle x,y \rangle} = \exp(\langle x,y \rangle \log (1+\epsilon)) $

which is a valid kernel.