Forecasting Multilinear Data via Transform-Based Tensor Autoregression
This addresses forecasting needs for big data applications such as image and video analysis, but appears incremental as it expands existing autoregressive techniques.
The paper tackles forecasting 2-dimensional data by developing L-Transform Tensor Autoregression (L-TAR), which combines time-series modeling with multilinear algebra to achieve statistical independence between columns via invertible discrete linear transforms, and validates it on datasets like images, videos, and stock prices.
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.