[Paper Review] A Simple Baseline Algorithm for Graph Classification

Nathan de Lara, Edouard Pineau|ArXiv.org|Oct 22, 2018

Graph Theory and AlgorithmsComputer Science13 references43 citations

TL;DR

The paper proposes a simple, fast baseline for graph classification using the smallest positive eigenvalues of the normalized Laplacian as spectral features, combined with a random forest classifier, achieving competitive results on standard datasets without heavy hyperparameter tuning.

ABSTRACT

Graph classification has recently received a lot of attention from various fields of machine learning e.g. kernel methods, sequential modeling or graph embedding. All these approaches offer promising results with different respective strengths and weaknesses. However, most of them rely on complex mathematics and require heavy computational power to achieve their best performance. We propose a simple and fast algorithm based on the spectral decomposition of graph Laplacian to perform graph classification and get a first reference score for a dataset. We show that this method obtains competitive results compared to state-of-the-art algorithms.

Motivation & Objective

• Motivate a lightweight baseline for graph classification that relies solely on graph structure without node features.
• Explore whether spectral properties of the normalized Laplacian can serve as effective graph embeddings for classification.
• Assess the performance and computation time of the proposed baseline against state-of-the-art graph classification methods.

Proposed method

• Construct the normalized Laplacian of each graph and compute its k smallest positive eigenvalues as spectral features (padding with zeros if needed).
• Represent a graph by the ordered spectrum (SF) which is permutation-invariant with respect to node labeling.
• Use a standard classifier (random forest with balanced class weights) on the spectral features as the baseline model.
• Evaluate robustness to embedding dimension k and to RFC hyperparameters via cross-dataset experiments.
• Compare against other graph classification methods (EMD, PM, FB, DyF, SGE) using datasets MT, PTC, EZ, PF, DD, NCI1.

Experimental results

Research questions

• RQ1 Does a simple, permutation-invariant spectral representation of graphs suffice for competitive graph classification without node features?
• RQ2 How do spectral feature dimensionality and classifier choices affect accuracy and robustness across standard graph datasets?
• RQ3 How does the proposed SF + RFC baseline compare to state-of-the-art graph classification methods in terms of accuracy and computation time?

Key findings

• SF + RFC achieves top performance on five of six datasets (MT, PTC, EZ, PF, NCI1).
• The baseline embedding with RFC is extremely fast to compute, with total experiment time under 5 minutes on the reported setup.
• Different embedding dimensions show that even small k (e.g., k=5) yield competitive results, with larger k offering marginal gains.
• The method does not require heavy per-dataset hyperparameter tuning and remains robust across RFC hyperparameters.
• Compared to other methods (EMD, PM, FB, DyF, SGE), SF + RFC shows competitive accuracy across multiple datasets.