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.

Motivated by electricity consumption reconstitution, we propose a new matrix recovery method using nonnegative matrix factorization (NMF). The task tackled here is to reconstitute electricity consumption time series at a fine temporal scale from measures that are temporal aggregates of individual consumption. Contrary to existing NMF algorithms, the proposed method uses temporal aggregates as input data, instead of matrix entries. Furthermore, the proposed method is extended to take into account individual autocorrelation to provide better estimation, using a recent convex relaxation of quadratically constrained quadratic programs. Extensive experiments on synthetic and real-world electricity consumption datasets illustrate the effectiveness of the proposed method.