The HIM glocal metric and kernel for network comparison and classification

TL;DR

This paper introduces the HIM metric and kernel, combining local and global graph comparison measures, to improve network classification and comparison across various scientific domains.

Contribution

The paper presents a novel graph distance metric and kernel that integrate local and global features, enhancing network comparison and classification methods.

Findings

HIM metric effectively combines local and global graph features.

HIM kernel improves network classification accuracy.

Applications demonstrate broad utility in biology and social networks.

Abstract

Due to the ever rising importance of the network paradigm across several areas of science, comparing and classifying graphs represent essential steps in the networks analysis of complex systems. Both tasks have been recently tackled via quite different strategies, even tailored ad-hoc for the investigated problem. Here we deal with both operations by introducing the Hamming-Ipsen-Mikhailov (HIM) distance, a novel metric to quantitatively measure the difference between two graphs sharing the same vertices. The new measure combines the local Hamming distance and the global spectral Ipsen-Mikhailov distance so to overcome the drawbacks affecting the two components separately. Building then the HIM kernel function derived from the HIM distance it is possible to move from network comparison to network classification via the Support Vector Machine (SVM) algorithm. Applications of HIM distance and HIM kernel in computational biology and social networks science demonstrate the effectiveness of the proposed functions as a general purpose solution.