000222804 001__ 222804
000222804 005__ 20190317000549.0
000222804 037__ $$aARTICLE 000222804 245__$$aStationary time-vertex signal processing
000222804 336__ $$aJournal Articles 000222804 520__$$aThe 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.
000222804 6531_ $$astationarity 000222804 6531_$$aultivariate time-vertex processes
000222804 6531_ $$aharmonic analysis 000222804 6531_$$agraph signal processing
000222804 6531_ $$aPSD estimation 000222804 700__$$0249911$$g266654$$aLoukas, Andreas
000222804 700__ $$aPerraudin, Nathanaël 000222804 773__$$tIEEE Transactions on Signal Processing
000222804 8564_ $$uhttps://infoscience.epfl.ch/record/222804/files/perraudin-note-016_1.pdf$$zPreprint$$s996130$$yPreprint
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000222804 917Z8 $$x266654 000222804 937__$$aEPFL-ARTICLE-222804
000222804 973__ $$rNON-REVIEWED$$sSUBMITTED$$aEPFL 000222804 980__$$aARTICLE