# Forecasting Multilinear Data via Transform-Based Tensor Autoregression

arXiv: https://arxiv.org/abs/2205.12201 · HTML: https://mlsanity.com/paper/2205.12201/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 31 references that are in the map.
- First posted on arXiv 24 May 2022.

## Builds on (most cited first, 1 of 1)

- [Transform-Based Multilinear Dynamical System for Tensor Time Series Analysis](https://mlsanity.com/paper/1811.07342/) (2018)

## Abstract (arXiv)

In the era of big data, there is an increasing demand for new methods for analyzing and forecasting 2-dimensional data. The current research aims to accomplish these goals through the combination of time-series modeling and multilinear algebraic systems. We expand previous autoregressive techniques to forecast multilinear data, aptly named the L-Transform Tensor autoregressive (L-TAR for short). Tensor decompositions and multilinear tensor products have allowed for this approach to be a feasible method of forecasting. We achieve statistical independence between the columns of the observations through invertible discrete linear transforms, enabling a divide and conquer approach. We present an experimental validation of the proposed methods on datasets containing image collections, video sequences, sea surface temperature measurements, stock prices, and networks.