SGL: Spectral Graph Learning from Measurements
This work addresses scalable graph learning for circuit design and optimization, offering a novel method but with incremental improvements over existing graphical Lasso approaches.
The paper tackles the problem of learning ultra-sparse resistor networks from linear measurements like node voltages and currents, proving that O(log N) measurements suffice to recover networks that preserve effective resistance distances and structural properties, with experiments showing high scalability without sacrificing quality.
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.