Abstract
Recent years have witnessed a rise in real-world data captured with rich structural information that can be conveniently depicted by multi-relational graphs. While inference of continuous node features across a simple graph is rather under-studied by the current relational learning research, we go one step further and focus on node regression problem on multi-relational graphs. We take inspiration from the well-known label propagation algorithm aiming at completing categorical features across a simple graph and propose a novel propagation framework for completing missing continuous features at the nodes of a multi-relational and directed graph. Our multi-relational propagation algorithm is composed of iterative neighborhood aggregations which originate from a relational local generative model. Our findings show the benefit of exploiting the multi-relational structure of the data in several node regression scenarios in different settings.
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Notes
- 1.
In directed graphs, symmetric relationships emerge from bi-directed edges where the edge direction is valid in both directions such as sibling whereas in asymmetric relationships, the edge direction is valid in only one direction such as parent, child. See the edge directions in Fig. 1.
- 2.
Generalization to vectorial node representations is possible in principle, yet omitted here for the sake of simplicity.
- 3.
Clamping step also exists in label propagation algorithm [20], which provides re-injection of true labels at each iteration throughout the propagation instead of overwriting the labeled nodes with the aggregated neighborhood information.
- 4.
Source code is available at https://github.com/bayrameda/MrAP. A special case of MrP is studied to propagate heterogeneous node features in [2] for numerical attribute completion in knowledge graphs.
- 5.
The label propagation algorithm [20] was originally designed for completing categorical features across a simple, weighted graph. We render it to propagate continuous features and to be applicable for the node regression by the default parameter set of MrP.
- 6.
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Bayram, E. (2022). Propagation on Multi-relational Graphs for Node Regression. In: Benito, R.M., Cherifi, C., Cherifi, H., Moro, E., Rocha, L.M., Sales-Pardo, M. (eds) Complex Networks & Their Applications X. COMPLEX NETWORKS 2021. Studies in Computational Intelligence, vol 1072. Springer, Cham. https://doi.org/10.1007/978-3-030-93409-5_14
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