Random Feature Approximation for Online Nonlinear Graph Topology Identification

TL;DR

This paper introduces an online kernel-based method using random feature approximation and group lasso optimization for nonlinear graph topology estimation, effectively handling high-dimensional data and sparse networks.

Contribution

It presents a novel online algorithm combining Fourier-based random features and group lasso for efficient nonlinear graph topology identification.

Findings

Outperforms existing methods on real and synthetic data.

Handles high-dimensional kernel representations efficiently.

Exploits network sparsity for improved accuracy.

Abstract

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.