Uncertainty Principle for Vertex-Time Graph Signal Processing

TL;DR

This paper introduces a unified uncertainty principle for vertex-time graph signals, enabling better signal localization, reconstruction, and graph topology inference in network data analysis.

Contribution

It unifies classical and graph uncertainty principles, defines vertex-time spectral spreads, and develops a new vertex-time dictionary and topology inference method.

Findings

Improved signal reconstruction accuracy

Enhanced robustness to noise in graph learning

Effective graph topology inference demonstrated on datasets

Abstract

We present an uncertainty principle for graph signals in the vertex-time domain, unifying the classical time-frequency and graph uncertainty principles within a single framework. By defining vertex-time and spectral-frequency spreads, we quantify signal localization across these domains. Our framework identifies a class of signals that achieve maximum concentration in both the spatial and temporal domains. These signals serve as fundamental atoms for a new vertex-time dictionary, enhancing signal reconstruction under practical constraints, such as intermittent data commonly encountered in sensor and social networks. Furthermore, we introduce a novel graph topology inference method leveraging the uncertainty principle. Numerical experiments on synthetic and real datasets validate the effectiveness of our approach, demonstrating improved reconstruction accuracy, greater robustness to noise, and enhanced graph learning performance compared to existing methods.