[Paper Review] A simple yet effective baseline for non-attributed graph classification

Chen Cai, Yusu Wang|arXiv (Cornell University)|Nov 8, 2018

Advanced Graph Neural Networks21 references42 citations

TL;DR

The paper introduces Local Degree Profile (LDP), a simple, linear-time graph representation based on local degree distributions that achieves competitive performance with state-of-the-art graph kernels and graph neural networks on non-attributed graphs, and remains a strong baseline for attributed graphs.

ABSTRACT

Graphs are complex objects that do not lend themselves easily to typical learning tasks. Recently, a range of approaches based on graph kernels or graph neural networks have been developed for graph classification and for representation learning on graphs in general. As the developed methodologies become more sophisticated, it is important to understand which components of the increasingly complex methods are necessary or most effective. As a first step, we develop a simple yet meaningful graph representation, and explore its effectiveness in graph classification. We test our baseline representation for the graph classification task on a range of graph datasets. Interestingly, this simple representation achieves similar performance as the state-of-the-art graph kernels and graph neural networks for non-attributed graph classification. Its performance on classifying attributed graphs is slightly weaker as it does not incorporate attributes. However, given its simplicity and efficiency, we believe that it still serves as an effective baseline for attributed graph classification. Our graph representation is efficient (linear-time) to compute. We also provide a simple connection with the graph neural networks. Note that these observations are only for the task of graph classification while existing methods are often designed for a broader scope including node embedding and link prediction. The results are also likely biased due to the limited amount of benchmark datasets available. Nevertheless, the good performance of our simple baseline calls for the development of new, more comprehensive benchmark datasets so as to better evaluate and analyze different graph learning methods. Furthermore, given the computational efficiency of our graph summary, we believe that it is a good candidate as a baseline method for future graph classification (or even other graph learning) studies.

Motivation & Objective

• Evaluate whether a simple local-information-based graph representation can perform well on non-attributed graph classification.
• Compare the LDP baseline to state-of-the-art graph kernels and graph neural networks across standard datasets.
• Assess the computational efficiency and scalability of the proposed approach as a baseline for graph classification.

Proposed method

• Compute for each node v: degree(v) and statistics (min, max, mean, std) of the degrees of its neighbors (DN(v)).
• Create graph-level features by applying either a histogram or an empirical distribution function to each of the five node features and concatenate across features.
• Train a linear or nonlinear SVM on the aggregated graph features with 10-fold cross-validation repeated ten times and report average accuracy.
• Analyze computational complexity: feature extraction is O(E) and mapping V values to B bins is O(V); discuss kernel-based and neural-network baselines for comparison.
• Discuss relation to Graph Neural Networks by showing LDP captures essential ingredients of GNNs without learning, and consider adding a potential extra feature like sum(DN(v)) (not deployed in final results).
• Hyperparameters include bin size, normalization strategy, representation (histogram vs empirical distribution), scale choice (linear vs log), and SVM parameters C and kernel bandwidth.

Experimental results

Research questions

• RQ1 Can a simple, non-learned local feature representation rival complex graph kernels and GNNs on non-attributed graph classification?
• RQ2 How does the LDP baseline compare to state-of-the-art methods across standard non-attributed graph datasets in terms of accuracy and efficiency?
• RQ3 What are the limitations of using only local, non-attribute information for graph classification, and when might global or attribute information be necessary?

Key findings

• The Local Degree Profile (LDP) baseline achieves competitive performance with state-of-the-art graph kernels and many graph neural networks on non-attributed graph classification tasks.
• Even with a linear SVM (no learning of representations), LDP performs well on several datasets, including Reddit variants.
• Adding additional node or edge features yields limited, dataset-wide improvements, suggesting that purely local degree-based features can be surprisingly powerful for non-attributed graphs, while more global/attribute information may be required for highly labeled datasets (e.g., some chemical graphs).
• LDP is computationally efficient with linear-time feature extraction, highlighting its suitability as a strong baseline for future graph classification studies and the need for larger, more comprehensive benchmarks.