A Comprehensive Evaluation of Graph Kernels for Unattributed Graphs.

Lulu Wang,Liandong Wang,Yi Zhang

doi:10.3390/e20120984

Abstract

Graph kernels are of vital importance in the field of graph comparison and classification. However, how to compare and evaluate graph kernels and how to choose an optimal kernel for a practical classification problem remain open problems. In this paper, a comprehensive evaluation framework of graph kernels is proposed for unattributed graph classification. According to the kernel design methods, the whole graph kernel family can be categorized in five different dimensions, and then several representative graph kernels are chosen from these categories to perform the evaluation. With plenty of real-world and synthetic datasets, kernels are compared by many criteria such as classification accuracy, F1 score, runtime cost, scalability and applicability. Finally, quantitative conclusions are discussed based on the analyses of the extensive experimental results. The main contribution of this paper is that a comprehensive evaluation framework of graph kernels is proposed, which is significant for graph-classification applications and the future kernel research.

Highlights

Graphs are important structures for information representation, in which nodes and edges respectively represent the entities and the relationships in the real world
Through classification tests on plenty of real-world and synthetic datasets, these graph kernels are compared by many criteria such as classification accuracy, F1 score, runtime cost, scalability and applicability
For the case of using discrete-time edge-based quantum walk (DTQW), the runtime cost is nearly the square of that of using RWK, which may be owing to the computation of the evolution of the quantum state

Summary

Introduction

Graphs are important structures for information representation, in which nodes and edges respectively represent the entities and the relationships in the real world. Graph processing has been widely used in many scientific fields such as image processing [1], biochemical research [2], social network [3] and natural language processing [4]. Graph comparison plays a core role in data mining and target recognition in these fields. Two molecules with the same chemical properties usually have similar topological structures [5]. People can successfully perform a prediction for an unknown molecule via topology comparison with known ones. It has been reported that exact graph comparison is equivalent to sub-graph isomorphism detection, which is a well-known NP-hard problem [6]. Inexact substitutions have to be explored, such as approximate graph edit distance [7], topological descriptors [8] and graph kernels

Methods

Results

Discussion

Conclusion