Functorial comparison of smooth graph signals via Grassmann geodesics

Counts differ because each database indexes a different set of publications. We treat OpenAlex as the canonical count; Google Scholar is not shown (no API, and crawling it violates its ToS).

Graph Signal Processing (GSP) extends classical signal processing techniques to signals defined on irregular, graph-structured domains. However, traditional GSP methods typically assume that all signals share a common underlying graph, an assumption that often fails in real-world scenarios. In this work, we propose a subspace approach for comparing graph signals with different and unknown underlying structures, thereby extending the scope of traditional GSP methods. Our approach adopts a functorial perspective, treating a set of graph signals as a sequence of functions defined on an unknown graph. We differentiate between sets of graph signals by analyzing their respective function subspaces. To quantify these differences, we utilize two operators, originally introduced in the context of computer graphics as functional maps. By recognizing the relationship between these operators and the Grassmann manifold, we define a similarity score that captures differences between the function subspaces. We validate our method on simulated graph models, demonstrating clear improvements over baseline approaches. Furthermore, we showcase its versatility across diverse applications, including fingerprinting and anomaly detection on functional MRI data and on multichannel and single-channel ECG signals.