Temporal Matrix Factorization for Multivariate Time Series Forecasting

Evaluate the model on fluid dynamic data and show the forecasting results with heatmaps

Temporal matrix factorization is an important variant in the large family of matrix factorization models. Thanks to the temporal modeling technique (e.g., vector autoregressive (VAR) process), temporal matrix factorization is extremely useful for multivariate time series forecasting in the presence of missing values. The basic idea behind the model is that matrix factorization can learn low-rank temporal patterns from partially observed time series data, while temporal modeling can capture time-evolving coefficients. In this blog post, we introduce a temporal matrix factorization model in [1–2] and try to forecast fluid dynamics with it. Since we provide Python implementation in this blog post, it would be easy to follow the content. Enjoy it! :)

Let’s get started!

Matrix Factorization

Matrix factorization is a powerful tool for reconstructing data matrices with missing entries. In the past few decades, there are many successful applications to recommender system and image inpainting. The fundamental idea is that a partially observed data matrix can be factorized into two factor matrices of relatively low-rank R.

In practice, the common dynamics of a large amount of time series could stem from a relatively small number of latent…