Forecasting Nonnegative Time Series via Sliding Mask Method (SMM) and Latent Clustered Forecast (LCF)

TL;DR

This paper introduces two novel nonnegative time series forecasting methods, SMM and LCF, leveraging matrix factorization and archetypal analysis, with theoretical guarantees and validated by experiments.

Contribution

It presents two new forecasting procedures based on NMF and archetypal analysis, with theoretical guarantees and demonstrated effectiveness.

Findings

SMM effectively predicts future values using matrix completion.

LCF improves forecasting by clustering and dimension reduction.

Both methods outperform existing approaches in experiments.

Abstract

We consider nonnegative time series forecasting framework. Based on recent advances in Nonnegative Matrix Factorization (NMF) and Archetypal Analysis, we introduce two procedures referred to as Sliding Mask Method (SMM) and Latent Clustered Forecast (LCF). SMM is a simple and powerful method based on time window prediction using Completion of Nonnegative Matrices. This new procedure combines low nonnegative rank decomposition and matrix completion where the hidden values are to be forecasted. LCF is two stage: it leverages archetypal analysis for dimension reduction and clustering of time series, then it uses any black-box supervised forecast solver on the clustered latent representation. Theoretical guarantees on uniqueness and robustness of the solution of NMF Completion-type problems are also provided for the first time. Finally, numerical experiments on real-world and synthetic data-set confirms forecasting accuracy for both the methodologies.