EigenNetworks

In many applications, the interdependencies among a set of $N$ time series $\{ x_{nk}, k>0 \}_{n=1}^{N}$ are well captured by a graph or network $G$. The network itself may change over time as well (i.e., as $G_k$). We expect the network changes to be at a much slower rate than that of the time series. This paper introduces eigennetworks, networks that are building blocks to compose the actual networks $G_k$ capturing the dependencies among the time series. These eigennetworks can be estimated by first learning the time series of graphs $G_k$ from the data, followed by a Principal Network Analysis procedure. Algorithms for learning both the original time series of graphs and the eigennetworks are presented and discussed. Experiments on simulated and real time series data demonstrate the performance of the learning and the interpretation of the eigennetworks.