Fast graph estimation method reduces computing time with some accuracy loss
Fast Graph Laplacian Estimation using Effective Resistance
Machine Learning
Summary
Figuring out the structure of a network from partial noisy information is hard, especially when there are fewer observations than nodes. The authors developed a new quick method to estimate the network connections by using a concept called effective resistance, avoiding slow repeated calculations. Their approach is not perfect in recovering every connection precisely but is much faster for networks of moderate size. This trade-off can make certain network analyses more practical.
What this means in practice
- •For network data analysts: Quickly estimate network connections from limited noisy data to speed up graph-based insights in social or sensor networks.
- •For signal processing engineers: Implement faster graph construction methods in graph signal processing pipelines to reduce computational overhead for medium-sized graphs.
Authors
Christoffer Kjellson, Claudio Altafini, Emma Tegling
Abstract
Inferring network topology from noisy node observations is a central problem in graph signal processing. In this paper, we consider Laplacian-constrained graph estimation for Gaussian Markov random fields, focusing on the underdetermined regime in which the number of samples is smaller than the number of graph nodes. Existing approaches often formulate the problem as a sparsity-regularized maximum-likelihood estimation problem. While effective, such methods typically require iterative optimization and are often computationally demanding, particularly under Laplacian constraints. Instead, we propose a non-iterative estimator of graph Laplacians that uses effective resistance for regularization, and evaluate the method using a simple sparsification procedure. Experiments show that with some trade-off in edge and weight recovery on the considered dataset, computational cost for moderately sized graphs can be substantially reduced.