#spectral

Question 1: Single choice

Kipf and Welling first derive the filter $\theta\,(I_N + D^{-1/2} A D^{-1/2})\,x$ , where $D$ is the diagonal degree matrix of the adjacency matrix $A$ . They then replace $I_N + D^{-1/2} A D^{-1/2}$ by $\tilde D^{-1/2}\tilde A\tilde D^{-1/2}$ , with $\tilde A = A + I_N$ and $\tilde D$ the degree matrix of $\tilde A$ (the renormalisation trick). Which problem of the first operator does this fix?

Its eigenvalues reach 2, so repeated use in deep models can explode or vanish1
It leaves out each node's own features, which only the self-loops of $\tilde A$ bring back2
It is not symmetric, so it has no orthonormal basis of eigenvectors to work with3
It needs an eigendecomposition of the graph Laplacian, which is too slow for large graphs4

Timed test