Canonical Correlation Analysis for Detecting Changes in Network Structure

Methods for the analysis of network data can be divided into two approaches, there are structural pattern recognition methods that act directly upon the relational data and alternatively the application of well studied standard statistical techniques which first require a transformation of the data to a vector representation. There are a number of methods available for the comparison of networks within the structural field, for example Frequent Sub graph Mining can be used to classify a collection of graphs into classes and spectral decomposition allows for anomaly detection. In this paper we detour from the standard structural methods and instead propose a novel combination of network embedding and Canonical Correlation Analysis(CCA) that allows comparison of coherent networks. We construct a test based on CCA that allows us to detect statistically significant differences between two graphs. This method is demonstrated on a number of simulated networks and also on the VAST Challenge 2008 cell phone call records data. These experiments suggest that the method is well suited for comparing networks of different types and hence is a new unsupervised method for graph comparison that does not look for specific changes in any one feature of a graph.