Collective Noise Filtering in Complex Networks

Abstract

Complex networks are powerful representations of complex systems across scales and domains, and the field is experiencing unprecedented growth in data availability. However, real-world network data often suffer from noise, biases, and missing data in edge weights, which undermine the reliability of downstream network analyses. Standard noise filtering approaches, whether treating individual edges one-by-one or assuming a uniform global noise level, are suboptimal, because in reality both signal and noise can be heterogeneous and correlated across multiple edges. As a solution, we introduce the Network Wiener Filter, a principled method for collective edge-level noise filtering that leverages both network structure and noise characteristics, to reduce error in the observed edge weights and to infer missing edge weights. We demonstrate the broad practical efficacy of the Network Wiener Filter in two distinct settings, the genetic interaction network of the budding yeast S. cerevisiae and the Enron Corpus email network, noting compelling evidence of successful noise suppression in both applications. With the Network Wiener Filter, we advocate for a shift toward error-aware network science, one that embraces data imperfection as an inherent feature and learns to navigate it effectively.