Forecasting Multilinear Data via Transform-Based Tensor Autoregression

@article{Cates2022ForecastingMD,
  title={Forecasting Multilinear Data via Transform-Based Tensor Autoregression},
  author={Jackson Cates and Randy C. Hoover and Kyle A. Caudle and Cagri Ozdemir and Karen S. Braman and David Machette},
  journal={ArXiv},
  year={2022},
  volume={abs/2205.12201}
}
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… 

References

SHOWING 1-10 OF 31 REFERENCES
Transform-Based Tensor Auto Regression for Multilinear Time Series Forecasting
TLDR
The current research expands previous auto-regressive techniques to forecast data from multilinear observations as oppose to scalars or vectors through invertible discrete linear transforms that enables statistical Independence between observations.
Multilinear Dynamical Systems for Tensor Time Series
TLDR
The multilinear dynamical system (MLDS) is presented for modeling tensor time series and an expectation-maximization (EM) algorithm to estimate the parameters.
Transform-Based Multilinear Dynamical System for Tensor Time Series Analysis
TLDR
The proposed multilinear dynamical system (MLDS) in a transform domain, named $\mathcal{L}$-MLDS, to model tensor time series is shown to achieve much higher prediction accuracy than the state-of-the-art MLDS and LDS with an equal number of parameters under different noise models.
Fourth-order Tensors with Multidimensional Discrete Transforms
TLDR
A novel multilinear tensor space that supports useful algorithms such as SVD and QR is built and a Householder QR algorithm is proposed to avoid the catastrophic cancellation problem associated with the conventional Gram-Schmidt process.
Tensor-Tensor Products with Invertible Linear Transforms
Fast Tensor Singular Value Decomposition Using the Low-Resolution Features of Tensors
TLDR
A computationally efficient approach for estimating the t-SVD by capitalizing on the correlations of the data in the temporal dimension by transforming the tensor data from the spatial domain to the spectral domain in order to obtain reduced order harmonic tensor.
2DTPCA: A New Framework for Multilinear Principal Component Analysis
TLDR
Experimental results are presented that show the proposed approach outperforms traditional “ tensor-based” PCA approaches with a much smaller subspace dimension in terms of recognition rates.
Third-Order Tensors as Operators on Matrices: A Theoretical and Computational Framework with Applications in Imaging
TLDR
This paper investigates further implications including a bilinear operator on the matrices which is nearly an inner product and which leads to definitions for length ofMatrices, angle between two matrices, and orthogonality of matrices and the use of t-linear combinations to characterize the range and kernel of a mapping defined by a third-order tensor and the t-product and the quantification of the dimensions of those sets.
Pose estimation from a single image using tensor decomposition and an algebra of circulants
TLDR
The current paper presents a new approach to dimensionality reduction and object classification of three-dimensional rigid objects based upon recent developments in tensor decompositions and a newly defined algebra of circulants.
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