A Persistent Homology Perspective to the Link Prediction Problem.

Persistent homology is a powerful tool in Topological Data Analysis (TDA) to capture topological properties of data succinctly at different spatial resolutions. For graphical data, shape and structure of the neighborhood of individual data items (nodes) is an essential means of characterizing their properties. We propose the use of persistent homology methods to capture structural and topological properties of graphs and use it to address the problem of link prediction. We achieve encouraging results on nine different real-world datasets that attest to the potential of persistent homology based methods for network analysis.