Nonnegative Matrix Factorization with Side Information for Time Series Recovery and Prediction

Motivated by the recovery and prediction of electricity consumption time series, we extend Nonnegative Matrix Factorization to take into account external features as side information. We consider general linear measurement settings, and propose a framework which models non-linear relationships betwe...

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Bibliographic Details
Published in:IEEE transactions on knowledge and data engineering 2019-03, Vol.31 (3), p.493-506
Main Authors: Mei, Jiali, De Castro, Yohann, Goude, Yannig, Azais, Jean-Marc, Hebrail, Georges
Format: Article
Language:English
Subjects:
Aggregates
Algorithms
Computer simulation
convex programming
Electricity
Electricity consumption
Estimation
Factorization
Kernel
Least squares
machine learning
Matrix decomposition
Prediction algorithms
Recommender systems
Recovery
signal processing
Signal processing algorithms
Time series
Time series analysis
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Summary:Motivated by the recovery and prediction of electricity consumption time series, we extend Nonnegative Matrix Factorization to take into account external features as side information. We consider general linear measurement settings, and propose a framework which models non-linear relationships between external features and the response variable. We extend previous theoretical results to obtain a sufficient condition on the identifiability of NMF with side information. Based on the classical Hierarchical Alternating Least Squares (HALS) algorithm, we propose a new algorithm (HALSX, or Hierarchical Alternating Least Squares with eXogeneous variables) which estimates NMF in this setting. The algorithm is validated on both simulated and real electricity consumption datasets as well as a recommendation system dataset, to show its performance in matrix recovery and prediction for new rows and columns.
ISSN:1041-4347
1558-2191
DOI:10.1109/TKDE.2018.2839678