A Time-Vertex Signal Processing Framework
This work addresses the challenge of handling high-dimensional non-Euclidean data for researchers in signal processing and machine learning, offering a novel framework with incremental improvements in filtering accuracy.
The paper tackles the problem of analyzing time-varying graph signals by introducing a Time-Vertex Signal Processing framework that integrates time-domain and graph signal processing, resulting in up to two orders of magnitude improvement in joint filtering accuracy and applications in tasks like dynamic mesh denoising and classification.
An emerging way to deal with high-dimensional non-euclidean data is to assume that the underlying structure can be captured by a graph. Recently, ideas have begun to emerge related to the analysis of time-varying graph signals. This work aims to elevate the notion of joint harmonic analysis to a full-fledged framework denoted as Time-Vertex Signal Processing, that links together the time-domain signal processing techniques with the new tools of graph signal processing. This entails three main contributions: (a) We provide a formal motivation for harmonic time-vertex analysis as an analysis tool for the state evolution of simple Partial Differential Equations on graphs. (b) We improve the accuracy of joint filtering operators by up-to two orders of magnitude. (c) Using our joint filters, we construct time-vertex dictionaries analyzing the different scales and the local time-frequency content of a signal. The utility of our tools is illustrated in numerous applications and datasets, such as dynamic mesh denoising and classification, still-video inpainting, and source localization in seismic events. Our results suggest that joint analysis of time-vertex signals can bring benefits to regression and learning.