Differential Network Analysis and Graph Classification: A Glocal Approach

Abstract

Based on the glocal HIM metric and its induced graph kernel, we propose a novel solution in differential network analysis that integrates network comparison and classification tasks. The HIM distance is defined as the one-parameter family of product metrics linearly combining the normalised Hamming distance H and the normalised Ipsen-Mikhailov spectral distance IM. The combination of the two components within a single metric allows overcoming their drawbacks and obtaining a measure that is simultaneously global and local. Furthermore, plugging the HIM kernel into a Support Vector Machine gives us a classification algorithm based on the HIM distance. First, we outline the theory underlying the metric construction. We introduce two diverse applications of the HIM distance and the HIM kernel to biological datasets. This versatility supports the adoption of the HIM family as a general tool for information extraction, quantifying difference among diverse in- stances of a complex system. An Open Source implementation of the HIM metrics is provided by the R package nettols and in its web interface ReNette.