Mix-hop Propagation in GNN

The mix-hop propagation layer has two steps1:

  1. information propagation step:

    $$ \mathbf H^{(k)} = \beta \mathbf H_{in} + (1-\beta)\mathbf L \mathbf H^{(k-1)}, $$

    where $\mathbf L= (1+ \operatorname{A}) (\mathbf A + \mathbf I)$. This convolution step tries to disentangle the correlation between the nodes.
  2. information selection step:

    $$ \mathbf H_{out} = \sum_k \mathbf H^{(k)} \mathbf W^{(k)}. $$

See Fig 4 in the paper1.

  1. Wu2020 Wu Z, Pan S, Long G, Jiang J, Chang X, Zhang C. Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks. arXiv [cs.LG]. 2020. Available: http://arxiv.org/abs/2005.11650  ↩︎

Planted: by ;

L Ma (2022). 'Mix-hop Propagation in GNN', Datumorphism, 11 April. Available at: https://datumorphism.leima.is/cards/forecasting/gnn-mix-hop-propagation/.