Sampling-Based Decomposition Algorithms for Arbitrary Tensor Networks

This repo contains code used in the experiment in the paper

O. A. Malik, V. Bharadwaj, R. Murray. Sampling-Based Decomposition Algorithms for Arbitrary Tensor Networks. Preprint arXiv:2210.03828, 2022.

A preprint is available on arXiv.

Referencing this code

If you use this code in any of your own work, please reference our paper:

@misc{malik2022TNS,
  doi = {10.48550/ARXIV.2210.03828},
  url = {https://arxiv.org/abs/2210.03828},
  author = {Malik, Osman Asif and Bharadwaj, Vivek and Murray, Riley},
  title = {Sampling-Based Decomposition Algorithms for Arbitrary Tensor Networks},
  publisher = {arXiv},
  year = {2022},
}

Some further details on the code

• experiment_TNS.m: This script runs the feature extraction experiment in our paper. It is an adaption of the script experiment_3.m in this repo.
• draw_samples_TNS_CP.m: This function draws the samples in the tensor network (TN) matrices that arise in CP decomposition. It is an adaption of the function draw_samples_CP.m in this repo.
• TNS_CP.m: This function computes the CP decomposition using the TN sampling approach we propose in the paper. It leverages the function draw_samples_TNS_CP.m above to do the actual sampling of the least squares problems. It is an adaption of the script cp_als_es.m in this repo.
• draw_samples_TNS_TR.m: This function draws the samples in the TN matrices that arise in tensor ring decomposition. It is an adaption of the function draw_samples_TR.m in this repo.
• TNS_TR.m: This function computes the tensor ring decomposition using the TN sampling approach we propose in the paper. It leverages the function draw_samples_TNS_TR.m above to do the actual sampling of the least squares problems. It is an adaption of the script tr_als_es.m in this repo.

Requirements

The code in this repo is reliant on code from the following two repositories:

• https://github.com/OsmanMalik/tr-als-sampled
• https://github.com/OsmanMalik/TD-ALS-ES

Before attempting to run the code in this repo, please ensure that both of the repos listed above are downloaded and made available in Matlab, e.g., via the addpath command. Also, ensure that all dependencies and requirements for those to repos are installed properly.

Author contact information

Please feel free to contact me at any time if you have any questions or would like to provide feedback on this code or on the paper. I can be reached at oamalik (at) lbl (dot) gov.