SGL: Spectral Graph Learning from Measurements

TL;DR

This paper presents a scalable spectral graph densification method for learning resistor networks from minimal linear measurements, effectively recovering sparse graphs that preserve spectral properties and effective resistance distances.

Contribution

Introduces a scalable spectral graph learning framework that recovers ultra-sparse resistor networks from limited measurements, connecting it to graphical Lasso problems.

Findings

Efficiently recovers sparse resistor networks with minimal measurements.

Preserves spectral and resistance distances of the original graph.

Highly scalable approach validated on real-world data.

Abstract

This work introduces a highly scalable spectral graph densification framework for learning resistor networks with linear measurements, such as node voltages and currents. We prove that given $O(\log N)$ pairs of voltage and current measurements, it is possible to recover ultra-sparse $N$-node resistor networks which can well preserve the effective resistance distances on the graph. Also, the learned graphs preserve the structural (spectral) properties of the original graph, which can potentially be leveraged in many circuit design and optimization tasks. We show that the proposed graph learning approach is equivalent to solving the classical graphical Lasso problems with Laplacian-like precision matrices. Through extensive experiments for a variety of real-world test cases, we show that the proposed approach is highly scalable for learning ultra-sparse resistor networks without sacrificing solution quality.