Online Graph Topology Inference with Kernels for Brain Connectivity Estimation

In graph signal processing, there are often settings where the graph topology is not known beforehand and has to be estimated from data. Moreover, some graphs can be dynamic, such as brain activity supported by neurons or brain regions. This paper focuses on estimating in an online and adaptive manner a network structure capturing the non-linear dependencies among streaming graph signals in the form of a possibly directed, adjacency matrix. By projecting data into a higher-or infinite-dimension space, we focus on capturing nonlinear relationships between agents. In order to mitigate the increasing number of data points, we employ kernel dictionaries. Finally, we run a series of tests in order to experimentally illustrate the usefulness of our kernel-based approach on biomedical data, on which we obtain results comparable to state-of-the-art methods.