A Harmonic Space Proofs

We prove only one direction. Since this is a constant vector, the two nodes are not separable in the diffusion limit.We state the following result without a proof (see Exercise 4.1 in Bishop [6]). If the sheaf has a trivial global section, all features converge to zero in the diffusion limit. The result follows from applying the trigonometric identity cos( π/ 2 + x) = sin x . Idea: We can use rotation matrices to align the harmonic features of the classes with the axis of coordinates as in Figure 6a. It can be checked that these matrices respect the properties outlined above.