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Edge-Based Graph Component Pooling

T. Snelleman, B. M. Renting, H. H. Hoos, J. N. van Rijn

TL;DR

This work proposes a pooling operator that merges nodes so as not to cause data loss but is also conceptually simple and computationally inexpensive, and outperform them on two popular benchmark datasets while reducing the number of learnable parameters on average.

Abstract

Graph-structured data naturally occurs in many research fields, such as chemistry and sociology. The relational information contained therein can be leveraged to statistically model graph properties through geometrical deep learning. Graph neural networks employ techniques, such as message-passing layers, to propagate local features through a graph. However, message-passing layers can be computationally expensive when dealing with large and sparse graphs. Graph pooling operators offer the possibility of removing or merging nodes in such graphs, thus lowering computational costs. However, pooling operators that remove nodes cause data loss, and pooling operators that merge nodes are often computationally expensive. We propose a pooling operator that merges nodes so as not to cause data loss but is also conceptually simple and computationally inexpensive. We empirically demonstrate that the proposed pooling operator performs statistically significantly better than edge pool on four popular benchmark datasets while reducing time complexity and the number of trainable parameters by 70.6% on average. Compared to another maximally powerful method named Graph Isomporhic Network, we show that we outperform them on two popular benchmark datasets while reducing the number of learnable parameters on average by 60.9%.

Edge-Based Graph Component Pooling

TL;DR

This work proposes a pooling operator that merges nodes so as not to cause data loss but is also conceptually simple and computationally inexpensive, and outperform them on two popular benchmark datasets while reducing the number of learnable parameters on average.

Abstract

Graph-structured data naturally occurs in many research fields, such as chemistry and sociology. The relational information contained therein can be leveraged to statistically model graph properties through geometrical deep learning. Graph neural networks employ techniques, such as message-passing layers, to propagate local features through a graph. However, message-passing layers can be computationally expensive when dealing with large and sparse graphs. Graph pooling operators offer the possibility of removing or merging nodes in such graphs, thus lowering computational costs. However, pooling operators that remove nodes cause data loss, and pooling operators that merge nodes are often computationally expensive. We propose a pooling operator that merges nodes so as not to cause data loss but is also conceptually simple and computationally inexpensive. We empirically demonstrate that the proposed pooling operator performs statistically significantly better than edge pool on four popular benchmark datasets while reducing time complexity and the number of trainable parameters by 70.6% on average. Compared to another maximally powerful method named Graph Isomporhic Network, we show that we outperform them on two popular benchmark datasets while reducing the number of learnable parameters on average by 60.9%.
Paper Structure (10 sections, 4 equations, 3 figures, 5 tables, 1 algorithm)

This paper contains 10 sections, 4 equations, 3 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Cluster Assignment Matrix generator
  5. Graph Coarsening
  6. Emperical Evaluation
  7. Datasets
  8. Setup of Experiments
  9. Results
  10. Conclusions & Future Work

Figures (3)

  • Figure 1: General illustration of our pooling operator $\mathcal{G}' = \mathrm{POOL}(\mathcal{G})$. Here we show how we create $\mathcal{G'} = \langle \mathcal{V'}, \mathcal{E'} \rangle$ from $\mathcal{G} = \langle \mathcal{V}, \mathcal{E} \rangle$ in two steps: We calculate the weights $W$ for every node using the edge scores and create the CAM $C$ using the graph component detection algorithm from Tarjan tarjan1972depth. We then coarsen the graph by combining the components into supernodes and removing the selected edges.
  • Figure 2: Boxplot visualization of the test set results shown in \ref{['tab:dataset_results']}, with accuracy on the y-axis. The results of our method and the methods we compare against are grouped per benchmark dataset on the x-axis.
  • Figure 3: Bar graph of the number of learnable parameters used per model, per benchmark, as seen in \ref{['tab:dataset_results_params']}. On the y-axis, we show the number of learnable parameters per model architecture of our method and the methods we compare against.