Nonnegative matrix factorization to find features in temporal networks

Abstract : Temporal networks describe a large variety of systems having a temporal evolution. Characterization and visualization of their evolution are often an issue especially when the amount of data becomes huge. We propose here an approach based on the duality between graphs and signals. Temporal networks are represented at each time instant by a collection of signals, whose spectral analysis reveals connection between frequency features and structure of the network. We use nonnegative matrix factorization (NMF) to find these frequency features and track them along time. Transforming back these features into subgraphs reveals the underlying structures which form a decomposition of the temporal network.