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Node Identifiers: Compact, Discrete Representations for Efficient Graph Learning

Yuankai Luo, Hongkang Li, Qijiong Liu, Lei Shi, Xiao-Ming Wu

TL;DR

A novel end-to-end framework that generates highly compact, discrete, and interpretable node representations, termed node identifiers (node IDs), to tackle inference challenges on large-scale graphs by employing vector quantization.

Abstract

We present a novel end-to-end framework that generates highly compact (typically 6-15 dimensions), discrete (int4 type), and interpretable node representations, termed node identifiers (node IDs), to tackle inference challenges on large-scale graphs. By employing vector quantization, we compress continuous node embeddings from multiple layers of a Graph Neural Network (GNN) into discrete codes, applicable under both self-supervised and supervised learning paradigms. These node IDs capture high-level abstractions of graph data and offer interpretability that traditional GNN embeddings lack. Extensive experiments on 34 datasets, encompassing node classification, graph classification, link prediction, and attributed graph clustering tasks, demonstrate that the generated node IDs significantly enhance speed and memory efficiency while achieving competitive performance compared to current state-of-the-art methods.

Node Identifiers: Compact, Discrete Representations for Efficient Graph Learning

TL;DR

A novel end-to-end framework that generates highly compact, discrete, and interpretable node representations, termed node identifiers (node IDs), to tackle inference challenges on large-scale graphs by employing vector quantization.

Abstract

We present a novel end-to-end framework that generates highly compact (typically 6-15 dimensions), discrete (int4 type), and interpretable node representations, termed node identifiers (node IDs), to tackle inference challenges on large-scale graphs. By employing vector quantization, we compress continuous node embeddings from multiple layers of a Graph Neural Network (GNN) into discrete codes, applicable under both self-supervised and supervised learning paradigms. These node IDs capture high-level abstractions of graph data and offer interpretability that traditional GNN embeddings lack. Extensive experiments on 34 datasets, encompassing node classification, graph classification, link prediction, and attributed graph clustering tasks, demonstrate that the generated node IDs significantly enhance speed and memory efficiency while achieving competitive performance compared to current state-of-the-art methods.
Paper Structure (33 sections, 1 theorem, 29 equations, 8 figures, 18 tables)

This paper contains 33 sections, 1 theorem, 29 equations, 8 figures, 18 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Our Proposed Node ID (NID) Framework
  4. Generation of Node IDs
  5. Applications of Node IDs for Graph Learning
  6. Theoretical Analysis
  7. Evaluation
  8. Overall Performance
  9. Supervised Node IDs for Supervised Representation Learning
  10. Self-supervised Node IDs for Unsupervised Representation Learning
  11. Analysis of Node IDs
  12. Related Works
  13. Conclusions
  14. Self-supervised Node IDs using GraphCL
  15. Proof of Theorem \ref{['thm: classification']}
  16. ...and 18 more sections

Key Result

Theorem 1

The optimizer $\boldsymbol{C}^*$ of VQ objective (loss) satisfies that, for any $\boldsymbol{x}_u$ and $\boldsymbol{x}_v$, $u,v\in\mathcal{V}$ with different labels, $\text{Node\_ID}(u)\neq \text{Node\_ID}(v)$. Then, as long as $\mathcal{V}_R$ uniformly include node IDs from all the classes, by trai

Figures (8)

  • Figure 1: Illustration of 2-dimensional node IDs generated by our NID framework using a two-layer GCN, with the first ID code derived from the node embedding in the first layer, and the second ID code derived from the node embeddings in the second layer. Center: t-SNE visualization of node embeddings in the PubMed Dataset, with colors representing different class labels. Left: Display of six nodes, each with their ID and 1-hop substructure. Nodes with the same first ID code share similar 1-hop structures, though this does not necessarily indicate the same class label. Right: Nodes E and F are further analyzed with their 2-hop substructures. Variations in these structures are reflected by their distinct second ID code (blue) and class label.
  • Figure 2: t-SNE visualization of the node representations of the Cora dataset generated by an MPNN at different layers $l$.
  • Figure 3: Overview of our proposed NID framework.
  • Figure 4: Supervised node classification results of $\textbf{NID}_\text{GCN}$ with varying ratios of training samples.
  • Figure 5: Codeword distributions of $c_{11}$ and $c_{21}$ in PubMed colored by the ground-truth labels.
  • ...and 3 more figures

Theorems & Definitions (2)

  • Theorem 1
  • proof