A Time-Vertex Signal Processing Framework: Scalable Processing and Meaningful Representations for Time-Series on Graphs - 2018


An rising approach to house high-dimensional noneuclidean data is to assume that the underlying structure can be captured by a graph. Recently, concepts have begun to emerge connected to the analysis of your time-varying graph signals. This Project 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 3 main contributions: a) We give a proper motivation for harmonic time-vertex analysis as an analysis tool for the state evolution of straightforward partial differential equations on graphs; b) we tend to improve the accuracy of joint filtering operators by up-to 2 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 sign. The utility of our tools is illustrated in various applications and datasets, like 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 advantages to regression and learning.

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