Forecasting Nonnegative Time Series via Sliding Mask Method (SMM) and Latent Clustered Forecast (LCF)
This work addresses forecasting for nonnegative time series, a domain-specific problem, with incremental improvements through hybrid methods.
The paper tackles nonnegative time series forecasting by introducing two new methods, Sliding Mask Method (SMM) and Latent Clustered Forecast (LCF), which combine nonnegative matrix factorization and archetypal analysis, and demonstrates their forecasting accuracy through numerical experiments on real-world and synthetic datasets.
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.