Analyzing Graph Time Series Using a Generative Model.

In this paper, we present a novel method for constructing a generative model to analyze the structure of labeled data. Given a time-series of sample graphs, we aim to learn a so-called “supergraph” that best describes the underlying average connectivity structure presenting in the data. In this time-series the vertex set is fixed and labeled and the set of possible connections between vertices change with time. The supergraph represents these changes with a Gaussian probability distribution for the connection weights on each individual edge. This structure is fitted to the time-series data by minimizing a description length criterion, with the von Neumann entropy controlling the complexity of the fitted model structure and the Gaussian log-likelihood controlling the mean edge weights and variances. We further show this fitting process can be optimized by using a new fixed-point iteration scheme which locates the elements of the optimal weighted adjacency matrix of the supergraph. We show the iteration process is in fact governed by the partial derivative of the von Neumann entropy. In the experiments, the resulting generative model is shown to be an effective tool for analyzing the underlying connectivity structure of time-evolving networks in the financial domain, and in particular locating critical events and distinct time epochs in their evolution.