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Revisiting Neighborhood Aggregation in Graph Neural Networks for Node Classification using Statistical Signal Processing

Mounir Ghogho

TL;DR

This work reconsiders neighborhood aggregation in graph neural networks for node classification under the edge-independent node-labels (EINL) assumption using a statistical signal processing perspective. It derives Bayes-optimal, single-layer classifiers under a homoscedastic Gaussian feature model, comparing weighted sum aggregation (WSA) and sum-then-concatenate aggregation (SCA), and showing that SCA can yield larger discriminative gains especially when graph structure meaningfully informs class separation. The paper extends the analysis to higher-order neighborhoods and to node-degree–dependent label correlations, providing analytical guidance on when and how to weight neighbor information and how normalization affects performance. Simulations corroborate the theoretical insights, highlighting that fixed GNN weights may be suboptimal when graph statistics vary with degree or class, and suggesting principled alternatives for robust, statistic-aware GNN design with practical parameter estimation considerations.

Abstract

We delve into the issue of node classification within graphs, specifically reevaluating the concept of neighborhood aggregation, which is a fundamental component in graph neural networks (GNNs). Our analysis reveals conceptual flaws within certain benchmark GNN models when operating under the assumption of edge-independent node labels, a condition commonly observed in benchmark graphs employed for node classification. Approaching neighborhood aggregation from a statistical signal processing perspective, our investigation provides novel insights which may be used to design more efficient GNN models.

Revisiting Neighborhood Aggregation in Graph Neural Networks for Node Classification using Statistical Signal Processing

TL;DR

This work reconsiders neighborhood aggregation in graph neural networks for node classification under the edge-independent node-labels (EINL) assumption using a statistical signal processing perspective. It derives Bayes-optimal, single-layer classifiers under a homoscedastic Gaussian feature model, comparing weighted sum aggregation (WSA) and sum-then-concatenate aggregation (SCA), and showing that SCA can yield larger discriminative gains especially when graph structure meaningfully informs class separation. The paper extends the analysis to higher-order neighborhoods and to node-degree–dependent label correlations, providing analytical guidance on when and how to weight neighbor information and how normalization affects performance. Simulations corroborate the theoretical insights, highlighting that fixed GNN weights may be suboptimal when graph statistics vary with degree or class, and suggesting principled alternatives for robust, statistic-aware GNN design with practical parameter estimation considerations.

Abstract

We delve into the issue of node classification within graphs, specifically reevaluating the concept of neighborhood aggregation, which is a fundamental component in graph neural networks (GNNs). Our analysis reveals conceptual flaws within certain benchmark GNN models when operating under the assumption of edge-independent node labels, a condition commonly observed in benchmark graphs employed for node classification. Approaching neighborhood aggregation from a statistical signal processing perspective, our investigation provides novel insights which may be used to design more efficient GNN models.
Paper Structure (12 sections, 32 equations, 4 figures)

This paper contains 12 sections, 32 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Graph modeling
  4. Node feature distribution modeling
  5. Graph-agnostic classifier
  6. Weighted sum aggregation
  7. Sum-then-concatenate aggregation
  8. Simulation results
  9. Extensions
  10. Higher-order neighborhood
  11. Node-dependent label-to-label correlations
  12. Discussion and Conclusions

Figures (4)

  • Figure 1: Candidate distributions before and after neighborhood aggregation, $\boldsymbol{x}_i+\boldsymbol{x}_j$, assuming pure homophily and $F=1$, in the unimodal and multimodal feature distribution cases.
  • Figure 2: Homophily level versus node degree.
  • Figure 3: Classification error probability of WSA and SCA and the optimum value of $\tilde{\alpha}_i$ for WSA versus $p_h$, assuming Special case 1; $\gamma_0=1$ (left) and $\gamma_0=10$ (right).
  • Figure 4: Classification error probability of WSA and SCA and the optimum value of $\Tilde{\alpha}$ versus the homophily level, $p_h$, assuming $M=4$, $\gamma_{0}(m,\ell)=4,\forall m\neq \ell$, in Special case 2 (left) and Special case 3 (right).