graph convolution

We define our convolutional graph filter (or linear shift-invariant) as follows. Let $S$ be a graph shift operator and $x$ some graph signal. Then a filter $H$ has

Note that means $H(S)$ is a $(K-1)$th degree polynomial of $S$ with (filter) coefficients $h_i$
^definition

This filter is

1. local (convolutional graph filters are local)
2. shift equivariant (convolutional graph filters are shift equivariant)
3. permutation invariant (convolutional graph filters are permutation equivariant)