A Unified Framework for Non-Negative Matrix and Tensor Factorisations with a Smoothed Wasserstein Loss

ICCVW 2021 pp. 4178-4186

doi:10.1109/ICCVW54120.2021.00466 /iccvw/2021/zhang2021iccvw-unified/

Abstract

Non-negative matrix and tensor factorisations are a classical tool for finding low-dimensional representations of high-dimensional datasets. In applications such as imaging, datasets can be regarded as distributions supported on a space with metric structure. In such a setting, a loss function based on the Wasserstein distance of optimal transportation theory is a natural choice since it incorporates the underlying geometry of the data. We introduce a general mathematical framework for computing non-negative factorisations of both matrices and tensors with respect to an optimal transport loss. We derive an efficient computational method for its solution using a convex dual formulation, and demonstrate the applicability of this approach with several numerical illustrations with both matrix and tensor-valued data.

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Cite

Text

Zhang. "A Unified Framework for Non-Negative Matrix and Tensor Factorisations with a Smoothed Wasserstein Loss." IEEE/CVF International Conference on Computer Vision Workshops, 2021. doi:10.1109/ICCVW54120.2021.00466

Markdown

[Zhang. "A Unified Framework for Non-Negative Matrix and Tensor Factorisations with a Smoothed Wasserstein Loss." IEEE/CVF International Conference on Computer Vision Workshops, 2021.](https://mlanthology.org/iccvw/2021/zhang2021iccvw-unified/) doi:10.1109/ICCVW54120.2021.00466

BibTeX

@inproceedings{zhang2021iccvw-unified,
  title     = {{A Unified Framework for Non-Negative Matrix and Tensor Factorisations with a Smoothed Wasserstein Loss}},
  author    = {Zhang, Stephen Y.},
  booktitle = {IEEE/CVF International Conference on Computer Vision Workshops},
  year      = {2021},
  pages     = {4178-4186},
  doi       = {10.1109/ICCVW54120.2021.00466},
  url       = {https://mlanthology.org/iccvw/2021/zhang2021iccvw-unified/}
}