Nonnegative matrix factorization with side information for time series recovery and prediction

TL;DR

This paper extends Nonnegative Matrix Factorization to incorporate side information for improved recovery and prediction of time series data, with theoretical guarantees and a new algorithm validated on real datasets.

Contribution

It introduces HALSX, a novel NMF algorithm that models non-linear relationships with side information, extending previous theoretical results for better identifiability.

Findings

Effective in reconstructing electricity consumption data

Accurately predicts new rows and columns in datasets

Validated on real and simulated datasets

Abstract

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.