Graph Edge Sampling
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Category: { Graph }
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Summary: Edge sampling is a technique to deal with weighted edges in large [[graph]] What is Graph Graph A graph $\mathcal G$ has nodes $\mathcal V$ and edges $\mathcal E$, $$ \mathcal G = ( \mathcal V, \mathcal E). $$ Edges Edges are relations between nodes. For $u\in \mathcal V$ and $v\in \mathcal V$, if there is an edge between them, then $(u, v)\in \mathcal E$. Representations of Graph There are different representations of a graph. Adjacency Matrix A adjacency matrix of a graph represents the nodes using row and column indices and edges using elements of the matrix. For simple graph, the … .
Pages: 22
Over-Smoothing in Graph Neural Networks
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Category: { Graph }
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Summary: Over-smoothing is the problem that the representations on each node of the graph neural networks becomes way too similar to each other.1 In Chapter 7 of Hamilton2020, the author interprets this phenomenon using the lower pass filter theory in signal processing, i.e., multiplying a signal by $\mathbf A^n$ is similar to a low-pass filter when $n$ is large, with $\mathbf A$ being the adjacency matrix.
Hamilton2020 Hamilton WL. Graph Representation Learning. Morgan & Claypool Publishers; 2020. pp. 1–159. doi:10.2200/S01045ED1V01Y202009AIM046 ↩︎
Pages: 22