Online Kernel-Based Graph Topology Identification with Partial-Derivative-Imposed Sparsity

In many applications, such as brain network connectivity or shopping recommendations, the underlying graph explaining the different interactions between participating agents is unknown. Moreover, many of these interactions may be based on nonlinear relationships, rendering the topology inference problem more complex. This paper presents a new topology inference method that estimates a possibly directed adjacency matrix in an online manner. In contrast to previous approaches which are based on additive models, the proposed model is able to explain general nonlinear interactions between the agents. Partial-derivative-imposed sparsity is implemented, while reproducing kernels are used to model nonlinearities. The impact of the increasing number of data points is alleviated by using dictionaries of kernel functions. A comparison with a previously developed method showcases the generality of the new model.