Elvin Isufi, Andreas Loukas, Nathanael Perraudin, Geert Leus
arXiv 19 Oct 2018 · eess.SP · publishedIEEE Transactions on Signal Processing (2019) · 113 citations (OpenAlex)
arXiv:1810.08581 · PDF · DOI · OpenAlex · Extracted main text
Graph-based techniques emerged as a choice to deal with the dimensionality issues in modeling multivariate time series. However, there is yet no complete understanding of how the underlying structure could be exploited to ease this task. This work provides contributions in this direction by considering the forecasting of a process evolving over a graph. We make use of the (approximate) time-vertex stationarity assumption, i.e., timevarying graph signals whose first and second order statistical moments are invariant over time and correlated to a known graph topology. The latter is combined with VAR and VARMA models to tackle the dimensionality issues present in predicting the temporal evolution of multivariate time series. We find out that by projecting the data to the graph spectral domain: (i) the multivariate model estimation reduces to that of fitting a number of uncorrelated univariate ARMA models and (ii) an optimal low-rank data representation can be exploited so as to further reduce the estimation costs. In the case that the multivariate process can be observed at a subset of nodes, the proposed models extend naturally to Kalman filtering on graphs allowing for optimal tracking. Numerical experiments with both synthetic and real data validate the proposed approach and highlight its benefits over state-of-the-art alternatives.
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| Reference | Intensity | Mentions | Sections | Main text | |
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| 30332.\protect\\ E-mail: see http://www.michaelshell.org/c… | unmatched citation key 30332.\protect\\ E-mail: see http://www.michaelshell.org/c… | 0.405 | 1 | 1 | 100% |
| Atlanta | unmatched citation key Atlanta | 0.405 | 1 | 1 | 100% |
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| Georgia Institute of Technology | unmatched citation key Georgia Institute of Technology | 0.405 | 1 | 1 | 100% |
| \IEEEcompsocthanksitem M. Shell was with the Department of… | unmatched citation key \IEEEcompsocthanksitem M. Shell was with the Department of… | 0.405 | 1 | 1 | 100% |
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| Citing paper | Intensity | Mentions | Sections | |
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| 1 | Vector AutoRegressive Moving Average Models: A Review | 0.405 | 1 | 1 |