Applying non-negative matrix factorization with covariates to multivariate time series data as a vector autoregression model

Abstract: Non-negative matrix factorization (NMF) is a powerful technique for dimensionality reduction, but its application to time series data remains limited. This paper proposes a novel framework that integrates NMF with a vector autoregression (VAR) model to capture both latent structure and temporal dependencies in multivariate time series data. By representing the NMF coefficient matrix as a VAR model, the framework leverages the interpretability of NMF while incorporating the dynamic characteristics of time series data. This approach allows for the extraction of meaningful features and accurate predictions in time series data.