graphon convolution

[[concept]]

Graphon convolution

Given a graphon signal $(W, X)$ , we write the graphon convolution as the map

\begin{aligned} T_{H} & : L_{2} ([0, 1]) \to L_{2} ([0, 1]) \\ T_{H} & : X \mapsto Y \end{aligned}

with

Y = T_{H} X = \sum_{k = 0}^{K - 1} h_{k} T_{W}^{(k)} X

and

T_{W}^{(k)} X = {\begin{cases} \int_{0}^{1} W (u, \cdot) (T_{W}^{(k - 1)} X) (u) d u & k \geq 1 \\ I & k = 0 \end{cases}

Mentions

File	Last Modified
2025-03-26 lecture 15	2025-10-02
2025-04-02 lecture 17	2025-10-02
2025-04-07 lecture 18	2025-10-02
2025-04-09 lecture 19	2025-10-02
convergence bound for graph convolutions	2025-10-02
graph convolutions of bandlimited signals converge to the graphon convolution	2025-10-02
graphon convolutions act pointwise in the spectral domain	2025-10-02
lipschitz graph convolutions of graph signals converge to lipschitz graphon filters	2025-10-02
Lipschitz graphon filter	2025-10-02
spectral representation of graphon convolutions	2025-10-02
the graph convolution converges to the graphon convolution in the spectral domain for a convergent sequence of graph signals	2025-10-02

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