222804
20190317000549.0
ARTICLE
Stationary time-vertex signal processing
Journal Articles
The goal of this paper is to improve learning for multivariate processes whose structure is dependent on some known graph topology. Typically, the graph information is incorporated to the learning process via a smoothness assumption postulating that the values supported on well connected vertices exhibit small variations. We argue that smoothness is not enough. To capture the behavior of complex interconnected systems, such as transportation and biological networks, it is important to train expressive models, being able to reproduce a wide range of graph and temporal behaviors. Motivated by this need, this paper puts forth a novel definition of time-vertex wide-sense stationarity, or joint stationarity for short. We believe that the proposed definition is natural, at it elegantly relates to existing definitions of stationarity in the time and vertex domains. We use joint stationarity to regularize learning and to reduce computational complexity in both estimation and recovery tasks. In particular, we show that for any jointly stationary process: (a) one can learn the covariance structure from O(1) samples, and (b) can solve MMSE recovery problems, such as interpolation, denoising, forecasting, in complexity that is linear to the edges and timesteps. Experiments with three datasets suggest that joint stationarity can yield significant accuracy improvements in the reconstruction effort.
stationarity
ultivariate time-vertex processes
harmonic analysis
graph signal processing
PSD estimation
249911
Loukas, Andreas
266654
Perraudin, NathanaĆ«l
IEEE Transactions on Signal Processing
996130
http://infoscience.epfl.ch/record/222804/files/perraudin-note-016_1.pdf
Preprint
Preprint
252392
LTS2
U10380
oai:infoscience.tind.io:222804
STI
article
GLOBAL_SET
179669
266654
EPFL-ARTICLE-222804
EPFL
NON-REVIEWED
SUBMITTED
ARTICLE