What can we do with a tensor factorization?

Question

I have three questions about tensor factorization.

1. what is the case(or application) for tensor factorization(decomposition)?
2. how likely is this to become a mainstream technology in the future?
3. how do you use it?

Answer 1

Tensor factorization is a powerful tool for modeling spatiotemporal data. To better understand tensor factorization and its applications, it is a good start to take an example by real-world traffic data imputation. In urban transportation systems, we could collect time series data indicating road traffic speed/volume from different spatial locations, and these data are indeed tensors. However, missing data problem is inevitable when collecting these data. Therefore, as shown in Figure 1, we provide a tensor completion based solution for missing traffic data imputation in our recent study.

Figure 1: Graphical illustration of the tensor completion task for partially observed traffic measurements.

Here, we also provide our Bayesian tensor factorization code for imputing missing traffic data (evaluated on publicly available Guangzhou traffic speed data set, Birmingham parking data set, Hangzhou metro passenger flow data set, and NYC taxi demand data set) with Python implementation (mainly supported by Numpy). If you want to learn more about Bayesian tensor factorization and its implementation, please consider reading the following items:

• How to impute spatiotemporal missing traffic data with Bayesian Gaussian tensor factorization in Python? (Jupyter Notebook)

• transdim (GitHub): transportation data imputation using machine learning models.

• X. Chen, Z. He, L. Sun (2019). A Bayesian tensor decomposition approach for spatiotemporal traffic data imputation. Transportation Research Part C: Emerging Technologies, 98: 73-84.

• X. Chen, Z. He, Y. Chen, et al. (2019). Missing traffic data imputation and pattern discovery with a Bayesian augmented tensor factorization model. Transportation Research Part C: Emerging Technologies, 104: 66-77.