An Evolution Kernel Method for Graph Classification through Heat Diffusion Dynamics

TL;DR

This paper introduces an evolution kernel method that models the dynamic evolution of complex systems through heat diffusion on graphs, improving classification accuracy by capturing temporal traits.

Contribution

It proposes a novel heat-driven temporal graph augmentation and a dynamic time-wrapping distance to better represent and compare system evolution for classification.

Findings

Significant accuracy improvements over baseline methods in real-world datasets.

Effective modeling of system evolution through heat kernel and DropNode techniques.

Enhanced ability to distinguish complex systems based on their evolutionary trajectories.

Abstract

Autonomous individuals establish a structural complex system through pairwise connections and interactions. Notably, the evolution reflects the dynamic nature of each complex system since it recodes a series of temporal changes from the past, the present into the future. Different systems follow distinct evolutionary trajectories, which can serve as distinguishing traits for system classification. However, modeling a complex system's evolution is challenging for the graph model because the graph is typically a snapshot of the static status of a system, and thereby hard to manifest the long-term evolutionary traits of a system entirely. To address this challenge, we suggest utilizing a heat-driven method to generate temporal graph augmentation. This approach incorporates the physics-based heat kernel and DropNode technique to transform each static graph into a sequence of temporal ones. This approach effectively describes the evolutional behaviours of the system, including the retention or disappearance of elements at each time point based on the distributed heat on each node. Additionally, we propose a dynamic time-wrapping distance GDTW to quantitatively measure the distance between pairwise evolutionary systems through optimal matching. The resulting approach, called the Evolution Kernel method, has been successfully applied to classification problems in real-world structural graph datasets. The results yield significant improvements in supervised classification accuracy over a series of baseline methods.