Let us assume we have linear elements $X = \{x_i\}_i^n$ on the d-sphere. Depending on the number of elements, we may find a configuration that is in expectation, orthogonal, subject to the minimization of $\Vert XX^T - I\Vert^2_F$, where $E_{x,y}[x^Ty] = 0$ and $E_{x,y}[(x^Ty)^2]$ is minimal.
In the case where we are restricted to features $\phi(x)$ in a RKHS, is there a similar analogy for orthogonal features? Here, we would have a Kernel matrix K with $K_{ij} = k(x_i, x_j)$ where minimizing $\Vert K - I\Vert^2_F$ and is similar to finding a tight frame if centered or minimal energy configuration (discrete energy on reflectable sets) given a Gaussian or IMQ kernel.
How may I interpret orthogonality in this setting? If $\langle \phi(x), \phi(y)\rangle_H$ = 0 then they are orthogonal in feature space?