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Position-Sensing Graph Neural Networks: Proactively Learning Nodes Relative Positions

Zhenyue Qin, Yiqun Zhang Saeed Anwar, Dongwoo Kim, Yang Liu, Pan Ji, Tom Gedeon

Abstract

Most existing graph neural networks (GNNs) learn node embeddings using the framework of message passing and aggregation. Such GNNs are incapable of learning relative positions between graph nodes within a graph. To empower GNNs with the awareness of node positions, some nodes are set as anchors. Then, using the distances from a node to the anchors, GNNs can infer relative positions between nodes. However, P-GNNs arbitrarily select anchors, leading to compromising position-awareness and feature extraction. To eliminate this compromise, we demonstrate that selecting evenly distributed and asymmetric anchors is essential. On the other hand, we show that choosing anchors that can aggregate embeddings of all the nodes within a graph is NP-complete. Therefore, devising efficient optimal algorithms in a deterministic approach is practically not feasible. To ensure position-awareness and bypass NP-completeness, we propose Position-Sensing Graph Neural Networks (PSGNNs), learning how to choose anchors in a back-propagatable fashion. Experiments verify the effectiveness of PSGNNs against state-of-the-art GNNs, substantially improving performance on various synthetic and real-world graph datasets while enjoying stable scalability. Specifically, PSGNNs on average boost AUC more than 14% for pairwise node classification and 18% for link prediction over the existing state-of-the-art position-aware methods. Our source code is publicly available at: https://github.com/ZhenyueQin/PSGNN.

Position-Sensing Graph Neural Networks: Proactively Learning Nodes Relative Positions

Abstract

Most existing graph neural networks (GNNs) learn node embeddings using the framework of message passing and aggregation. Such GNNs are incapable of learning relative positions between graph nodes within a graph. To empower GNNs with the awareness of node positions, some nodes are set as anchors. Then, using the distances from a node to the anchors, GNNs can infer relative positions between nodes. However, P-GNNs arbitrarily select anchors, leading to compromising position-awareness and feature extraction. To eliminate this compromise, we demonstrate that selecting evenly distributed and asymmetric anchors is essential. On the other hand, we show that choosing anchors that can aggregate embeddings of all the nodes within a graph is NP-complete. Therefore, devising efficient optimal algorithms in a deterministic approach is practically not feasible. To ensure position-awareness and bypass NP-completeness, we propose Position-Sensing Graph Neural Networks (PSGNNs), learning how to choose anchors in a back-propagatable fashion. Experiments verify the effectiveness of PSGNNs against state-of-the-art GNNs, substantially improving performance on various synthetic and real-world graph datasets while enjoying stable scalability. Specifically, PSGNNs on average boost AUC more than 14% for pairwise node classification and 18% for link prediction over the existing state-of-the-art position-aware methods. Our source code is publicly available at: https://github.com/ZhenyueQin/PSGNN.

Paper Structure

This paper contains 19 sections, 6 equations, 4 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Graph Neural Networks
  5. Relative Positions Learning
  6. Our Approaches
  7. Problem Formulation
  8. Position-Sensing Graph Neural Network
  9. Anchor Selection Component
  10. Positional Feature Learning Component
  11. Working Mechanisms
  12. Experiment
  13. Datasets and Tasks
  14. Experimental Setups
  15. Comparison Against State-of-the-Art
  16. ...and 4 more sections

Figures (4)

  • Figure 1: Samples of the selected anchors by the P-GNN you2019position (left) and the PSGNN proposed in this paper (right) for the connected Caveman graph. The anchors are highlighted in red. The anchors chose by the PSGNN distribute evenly in different communities without having symmetric anchors, whereas the ones by the P-GNN randomly scatter and induces symmetry.
  • Figure 2: Illustration of symmetric node positions. The two blue nodes are in symmetric locations within each graph. The dotted blue node represents an anchor.
  • Figure 3: Illustration of the covered nodes (yellow nodes) of anchors (red nodes).
  • Figure 4: Training process of a PSGNN. Dotted notes represent anchors.