Recovering Multiple Nonnegative Time Series From a Few Temporal   Aggregates
  Motivated by electricity consumption metering, we extend existing nonnegative matrix factorization (NMF) algorithms to use linear measurements as observations, instead of matrix entries. The objective is to estimate multiple time series at a fine temporal scale from temporal aggregates measured on each individual series. Furthermore, our algorithm is extended to take into account individual autocorrelation to provide better estimation, using a recent convex relaxation of quadratically constrained quadratic program. Extensive experiments on synthetic and real-world electricity consumption datasets illustrate the effectiveness of our matrix recovery algorithms. 
Jiali Mei, Yohann De Castro, Yannig Goude, Georges H\'ebrail
stat.ML