Forecasting Multilinear Data via Transform-Based Tensor Autoregression

TL;DR

This paper introduces the L-Transform Tensor autoregressive (L-TAR) model, which leverages multilinear algebra and invertible transforms to forecast complex 2D data like images, videos, and temperature measurements effectively.

Contribution

It extends autoregressive models to multilinear data using tensor decompositions and transforms, enabling scalable and independent-column forecasting.

Findings

Effective forecasting on diverse datasets including images and temperature data

Demonstrated statistical independence between columns via invertible transforms

Validated approach through extensive experiments

Abstract

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.