Nonnegative matrix factorization with side information for time series recovery and prediction
This work addresses matrix recovery and prediction challenges in domains like energy consumption and recommendation systems, but it is incremental as it builds on existing NMF methods by adding side information.
The authors tackled the problem of reconstructing and predicting time series data, such as electricity consumption, by extending Nonnegative Matrix Factorization (NMF) to incorporate side information like features, and proposed a new algorithm (HALSX) that improved performance in matrix recovery and prediction tasks, achieving validation on simulated and real datasets.
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.