Analyzing graphs by representing them in a low dimensional space using Graph Neural Networks (GNNs) is a promising research problem, with a lot of ongoing research. In this paper, we propose GraphReach, a position-aware GNN framework that captures the global positioning of nodes with respect to a set of fixed nodes , referred to as anchors. The model incorporates the reachability of nodes from anchors and vice versa, captured through multiple random walks. We use random walk since it captures the locality better. An extensive experimental evaluation comparing different variants of the model provides an insight into its ability to perform well on the downstream prediction tasks. GraphReach significantly outperforms the current state-of-the-art models and achieves an improvement of up to 31 and 11 percentage points, measured in ROC AUC, for the standard pairwise node classification and link prediction tasks, respectively .
Learning feature space node embeddings that encode the position of a node within the context of a graph is useful in several graph prediction tasks. Majority of the existing graph neural networks (GNN) learn node embeddings that encode their local neighborhoods but not their positions. Consequently, two nodes that are vastly distant but located in similar local neighborhoods would map to similar embeddings. This limitation may prevent accurate performance in predictive tasks that rely on position information. In this paper, we address this gap by developing GraphReach, a position-aware , inductive GNN. GraphReach captures the global positions of nodes though reachability estimations with respect to a set of nodes called anchors. The reachability estimations compute the frequency with which a node may visit an anchor through any possible path. The anchors are strategically selected so that the reachability estimations across all nodes are maximized. We show that this combinatorial anchor selection problem is NP-hard and consequently, develop a greedy (1-1/e) approximation. An extensive experimental evaluation covering six datasets and five state-of-the-art GNN architectures reveal that GraphReach is consistently superior and provides up to 40\% relative improvement in the predictive tasks of link prediction and pairwise node classification . In addition, GraphReach is more robust against adversarial attacks .
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Analyzing graphs by representing them in a low dimensional space using Graph Neural Networks (GNNs) is a promising research problem, with a lot of ongoing research.
Learning feature space node embeddings that encode the position of a node within the context of a graph is useful in several graph prediction tasks. Majority of the existing graph neural networks (GNN) learn node embeddings that encode their local neighborhoods but not their positions. Consequently, two nodes that are vastly distant but located in similar local neighborhoods would map to similar embeddings. This limitation may prevent accurate performance in predictive tasks that rely on position information.
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propose
address this gap by developing
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GNN framework that
, inductive GNN. GraphReach
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positioning of nodes
positions of nodes though reachability estimations
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fixed nodes , referred to as
nodes called
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model incorporates the reachability of nodes from anchors and vice versa, captured through multiple random walks. We use random walk since it captures the locality better.
reachability estimations compute the frequency with which a node may visit an anchor through any possible path. The anchors are strategically selected so that the reachability estimations across all nodes are maximized. We show that this combinatorial anchor selection problem is NP-hard and consequently, develop a greedy (1-1/e) approximation.
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comparing different variants of the model provides an insight into its ability to perform well on the downstream prediction tasks. GraphReach significantly outperforms the current
covering six datasets and five
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models and achieves an improvement of up to 31 and 11 percentage points, measured in ROC AUC, for the standard
GNN architectures reveal that GraphReach is consistently superior and provides up to 40\% relative improvement in the predictive tasks of link prediction and
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and link prediction tasks, respectively
. In addition, GraphReach is more robust against adversarial attacks