Random Feature Approximation for Online Nonlinear Graph Topology Identification
This work addresses online nonlinear graph topology identification, which is incremental as it builds on existing kernel and sparsity methods for real-world network applications.
The paper tackled the problem of online topology estimation for graph-connected time series with nonlinear dependencies by proposing a kernel-based algorithm using random feature approximation and group lasso optimization, and it outperformed competitors in experiments on real and synthetic data.
Online topology estimation of graph-connected time series is challenging, especially since the causal dependencies in many real-world networks are nonlinear. In this paper, we propose a kernel-based algorithm for graph topology estimation. The algorithm uses a Fourier-based Random feature approximation to tackle the curse of dimensionality associated with the kernel representations. Exploiting the fact that the real-world networks often exhibit sparse topologies, we propose a group lasso based optimization framework, which is solve using an iterative composite objective mirror descent method, yielding an online algorithm with fixed computational complexity per iteration. The experiments conducted on real and synthetic data show that the proposed method outperforms its competitors.