star-M-opt

This repository contains code for learning optimal tensor-tensor products using the star-M product introduced in Tensor–tensor products with invertible linear transforms.

Installation

Clone the repository using

git clone https://github.com/elizabethnewman/star-M-opt.git

Setup

To setup the paths, open MATLAB, make star-M-opt the working directory, and run

starMOptSetup

in the MATLAB console.

Required Matlab Toolboxes

• Financial Toolbox, Datafeed Toolbox
• PDE Toolbox

Organization:

• optimizers: options for optimization algorithms (gradient descent, alternating descent).
• objectiveFunctions: options for problem-specific objective functions (least squares, low-rank approximation) to pass to optimizer.
• products: functions for tensor-tensor (star-M, facewise) and tensor-matrix (mode-k) products.
• tensorSVD: functions to compute the tensor SVD and corresponding Jacobians.
• examples: examples applying optimal tensor-tensor products to various applications.
• utils: additional tools for tensor operations (folding/unfolding, Frobenius norm, transpose).
• unitTests: unit tests for other functions in repository. To test, run starMOptUnitTests in a MATLAB console.
• tutorials: introductory tutorials to demonstrate code functions.

Introductory Materials

To illustrate the functions available in this repository, we have provided some tutorials formatted as .mlx live scripts.

How to cite

@misc{newman2024optimalmatrixmimetictensoralgebras,
      title={Optimal Matrix-Mimetic Tensor Algebras via Variable Projection}, 
      author={Elizabeth Newman and Katherine Keegan},
      year={2024},
      eprint={2406.06942},
      archivePrefix={arXiv},
      primaryClass={math.NA},
      url={https://arxiv.org/abs/2406.06942}, 
}