What is the difference between the multivariate datasets and the multidimensional datasets？

[duansanshi]

Recently I have read some articles about data imputation，and found that some methods are for multivariate data while others for multidimensional data,I wonder what is the difference between these.Could you please give me a simple example? Thanks a lot !

[xinychen]

Thank you for this comment! Generally speaking, multivariate time series are in the form of matrix with N variables in which each variable is of length T. Multidimensional time series are in the form of tensor with M-by-N variables in which each variable is of length T. I would like to recommend our blog post for explaining these basic concepts, please check out Matrix Autoregressive Model for Multidimensional Time Series Forecasting.

[duansanshi]

Really thanks for answering so quickly！Now I can tell them apart. btw，I find another similar term called spatiotemporal data.（PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputation). I wonder whether it is the same conception as multidimensional time-series.Thanks again for helping me！

[xinychen]

Spatiotemporal data show more complicated dimensions, at least including spatial dimension and temporal dimension. In the modeling process, one is required to consider both spatial and temporal correlations. In terms of data format, there are some spatiotemporal data that are in the form of both multivariate and multidimensional time series. If you are interested, our recent study about Discovering dynamic patterns from spatiotemporal data with time-varying low-rank autoregression may give you some examples.