Curious if there is a proof or counter for whether the following function is a positive semidefinite kernel function.
$K(x,y) = \max\left(b_0 - b_1 \frac{|x-y|}{x+y}, 0\right)$
with $x > 0, y > 0, b_0 \in [0,1], b_1 \in [0, 1]$.
From simulating random vectors and random values of $b_0, b_1$ and then forming the kernel matrix with the function, it appears that it is PSD.
My intuition here is that this is a decreasing function in relative distance between $x$ and $y$, as $\frac{|x-y|}{x+y} \in [0,1]$, and similar in flavor to the Abel kernel $K(x,y)=e^{-\alpha |x-y|}$.