Recovering Multiple Nonnegative Time Series From a Few Temporal Aggregates

TL;DR

This paper develops advanced nonnegative matrix factorization algorithms to accurately recover multiple fine-scale time series from limited aggregate measurements, incorporating autocorrelation for improved estimation.

Contribution

It introduces a novel NMF-based approach that uses linear measurements instead of matrix entries and accounts for autocorrelation, enhancing recovery of time series from aggregates.

Findings

Effective recovery demonstrated on synthetic datasets.

Successful application to real-world electricity data.

Improved estimation accuracy with autocorrelation modeling.

Abstract

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.