A Time-Vertex Signal Processing Framework: Scalable Processing and Meaningful Representations for Time-Series on Graphs

An emerging way to deal with high-dimensional noneuclidean 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 paper aims to elevate the notion of joint harmonic analysis to a ful...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 66; no. 3; pp. 817 - 829
Main Authors: Grassi, Francesco, Loukas, Andreas, Perraudin, Nathanael, Ricaud, Benjamin
Format: Journal Article
Language:English
Published: IEEE 01.02.2018
Subjects:
Fourier transforms
graph signal processing
Graphical models
Harmonic analysis
Laplace equations
partial differential equations
Signal processing algorithms
Time-vertex signal processing
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:An emerging way to deal with high-dimensional noneuclidean 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 paper 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.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2017.2775589