Attributed Network Clustering: a Topological Data Analysis Approach

Abstract

This project proposes a new method to analyze attributed network data using the tools from topological data analysis along with other methods from network analysis. Attributed networks refer to network where each vertex in the network contain a list of features. The most common networks of this type of social networks such as facebook. We then break up the network into smaller subnetworks called ego-network centered around each individual vertex. We then apply a diffusion mapping to convert the attribute network into a weighted graph. We are then able to use the diffusion values to compute homology groups associated with each vertex. These homology groups contain the information about the shape of the data. We then use the Wasserstein distances to cluster the nodes using a hierarchical clustering algorithm. This project is very interesting from a network analysts viewpoint as it provides a completely new method of clustering attributed network data. Being able to accurate detect clusters in datasets such as facebook is very valuable. This project is also significant from a topological data analyst's view since it provides a method of applying the other tools of topological data analysis to attributed network data.