the spectral graph filter operates on a signal pointwise

Data

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

Remark

The spectral representation of a convolutional graph filter $\widehat{H(S)}$ is pointwise in the spectral domain. ie ${\hat{y}}_i={\sum }_{k=0}^{K-1}{h}_k{\lambda }_i^k{\hat{x}}_i$. This follows immediately from the fact that $\Lambda$ is diagonal.

$i$th spectral component of output $y$ only depends on ${\lambda }_i$ and ${\hat{x}}_i$

By inspection: the

Mentions

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