A Survey on Graph Kernels (1903.11835v2)

Abstract: Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We describe and categorize graph kernels based on properties inherent to their design, such as the nature of their extracted graph features, their method of computation and their applicability to problems in practice. In an extensive experimental evaluation, we study the classification accuracy of a large suite of graph kernels on established benchmarks as well as new datasets. We compare the performance of popular kernels with several baseline methods and study the effect of applying a Gaussian RBF kernel to the metric induced by a graph kernel. In doing so, we find that simple baselines become competitive after this transformation on some datasets. Moreover, we study the extent to which existing graph kernels agree in their predictions (and prediction errors) and obtain a data-driven categorization of kernels as result. Finally, based on our experimental results, we derive a practitioner's guide to kernel-based graph classification.

• The paper presents a comprehensive review of graph kernels, categorizing them by design, feature extraction, and computational methods for graph classification.
• It details practical evaluations that compare kernel performance, revealing trade-offs between expressivity and computational complexity.
• The paper offers actionable recommendations and outlines future research directions to enhance kernel efficiency for large-scale graph datasets.

Overview of the "Survey on Graph Kernels" Paper

In the domain of machine learning and data mining, the paper of graph-structured data has garnered significant attention. The paper "Survey on Graph Kernels" by Nils M. Kriege, Christopher Morris, and Fredrik D. Johansson provides a comprehensive review of graph kernels, which are pivotal tools for graph classification tasks. Graphs serve as a crucial representation in various domains where relationships among entities rather than individual attributes are of primary concern, such as bioinformatics, chemoinformatics, and social network analysis. The paper elucidates the design, evaluation, and application of graph kernels developed over the past decade and a half, offering a foundational reference for researchers and practitioners dealing with graph-based data.

Categorization and Evaluation of Graph Kernels

The paper adopts a systematic approach to categorize graph kernels based on their design paradigms, feature extraction methods, and computational methodologies. Key categories include:

• Neighborhood Aggregation Kernels: These kernels, such as the Weisfeiler-Lehman (WL) subtree kernel, leverage local neighborhood information to iteratively update vertex attributes, offering an efficient means to distill graph structure into rich feature vectors. This category also covers extensions and variants aimed at enhancing expressivity and computation.
• Assignment and Matching Kernels: The optimal assignment (OA) kernel is a significant focus here, where vertices between graphs are mapped for maximum similarity, often leading to non-positive semidefinite kernels. The paper discusses strategies to mitigate such issues, like prototype-based methods or the use of strong base kernels.
• Kernels Based on Subgraph Patterns: Graphlet kernels fall into this category, utilizing fixed-size subgraph patterns to measure similarity between graphs. The inherent trade-off between expressivity and computational complexity is acknowledged, with potential approximations explored for scalability.
• Walks and Paths Kernels: This includes both random walk and shortest-path kernels, which analyze vertex sequences or paths, though they often involve computationally intensive matrix operations.
• Kernels for Attributed Graphs: The paper highlights methods, including the GraphHopper and GraphInvariant kernels, that effectively integrate vertex and edge attributes with the graph structure in the similarity assessment.

Experimental Analysis and Practitioner's Guide

The paper provides an in-depth experimental comparison of several state-of-the-art graph kernels on benchmark datasets. The paper examines:

• Expressivity: By computing completeness ratios, the paper evaluates whether kernels can distinguish graphs based on structure and labels. The results underline the balance between increasing expressivity and preventing overfitting.
• Non-linear Transformations: The application of non-linear decision boundaries through the Gaussian RBF kernel is investigated, demonstrating that it can enhance classification accuracy for certain kernels.
• Practical Recommendations: A practitioner's guide is provided, recommending kernels based on dataset properties such as graph size, attribute importance, and dataset volume. The guidance assists in selecting suitable kernels under varied application scenarios.

Conclusions and Implications

The survey establishes that no single kernel outperforms others universally, emphasizing the need for careful kernel selection tailored to the dataset's graph properties and learning objectives. This work not only offers an extensive overview of graph kernels but also posits future research directions toward improving kernel efficiency and scalability, especially given the increasing sizes and complexities of graph datasets in practical applications.

Future Directions

Future research pathways involve developing more computationally efficient kernels for very large graphs, enhancing the treatment of continuous vertex attributes, and integrating deep learning approaches with traditional kernel methods to capitalize on their complementary strengths. As datasets and applications continue to evolve, so must the tools designed to analyze them, with graph kernels remaining a critical component in the machine learning toolkit.