graph convolution

Data

subject:: Data Science Methods for Large Scale Graphs parent:: Graph Signals and Graph Signal Processing theme:: math notes

Linear Shift-Invariant /Convolutional Graph Filters

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 $y=H(S)x={\sum }_{k=0}^{K-1}{h}_k{S}^{k}x,h_0,h_1,\dots ,h_{K-1}\in \mathbb{R}$ Note that means $H(S)$ is a $(K-1)$th degree polynomial of $S$ with (filter) coefficients $h_i$

Properties

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)

Mentions

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