Nonnegative matrix factorization with side information for time series recovery and prediction

Abstract : Motivated by the reconstruction and the prediction of electricity consumption, we extend Nonnegative Matrix Factorization~(NMF) to take into account side information (column or row features). We consider general linear measurement settings, and propose a framework which models non-linear relationships between features and the response variables. We extend previous theoretical results to obtain a sufficient condition on the identifiability of the NMF in this setting. Based the classical Hierarchical Alternating Least Squares~(HALS) algorithm, we propose a new algorithm (HALSX, or Hierarchical Alternating Least Squares with eXogeneous variables) which estimates the factorization model. The algorithm is validated on both simulated and real electricity consumption datasets as well as a recommendation dataset, to show its performance in matrix recovery and prediction for new rows and columns.
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https://hal.inria.fr/hal-01686429
Contributor : Yohann de Castro <>
Submitted on : Wednesday, January 17, 2018 - 1:23:48 PM
Last modification on : Friday, October 11, 2019 - 8:22:42 PM

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  • HAL Id : hal-01686429, version 1
  • ARXIV : 1709.06320

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Jean-Marc Azaïs, Yohann de Castro, Yannig Goude, Georges Hébrail, Jiali Mei. Nonnegative matrix factorization with side information for time series recovery and prediction. IEEE Transactions on Knowledge and Data Engineering, Institute of Electrical and Electronics Engineers, 2018. ⟨hal-01686429⟩

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