  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.
