Neighborhood Preserving Kernels for Attributed Graphs

TL;DR

This paper introduces a novel neighborhood preserving kernel for attributed graphs that combines attribute and label information, extending to shortest paths, and demonstrates superior performance on real-world datasets.

Contribution

The paper proposes a new kernel design that preserves neighborhood structures in attributed graphs and integrates multiple kernel components for enhanced similarity measurement.

Findings

Kernel value can be computed recursively using Weisfeiler-Lehman algorithm.

The proposed kernel outperforms state-of-the-art kernels on real-world datasets.

Extension to shortest paths maintains neighborhood properties in the kernel.

Abstract

We describe the design of a reproducing kernel suitable for attributed graphs, in which the similarity between the two graphs is defined based on the neighborhood information of the graph nodes with the aid of a product graph formulation. We represent the proposed kernel as the weighted sum of two other kernels of which one is an R-convolution kernel that processes the attribute information of the graph and the other is an optimal assignment kernel that processes label information. They are formulated in such a way that the edges processed as part of the kernel computation have the same neighborhood properties and hence the kernel proposed makes a well-defined correspondence between regions processed in graphs. These concepts are also extended to the case of the shortest paths. We identified the state-of-the-art kernels that can be mapped to such a neighborhood preserving framework. We found that the kernel value of the argument graphs in each iteration of the Weisfeiler-Lehman color refinement algorithm can be obtained recursively from the product graph formulated in our method. By incorporating the proposed kernel on support vector machines we analyzed the real-world data sets and it has shown superior performance in comparison with that of the other state-of-the-art graph kernels.