# Wasserstein Nonnegative Tensor Factorization with Manifold Regularization

arXiv: https://arxiv.org/abs/2401.01842 · HTML: https://mlsanity.com/paper/2401.01842/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 33 references that are in the map.
- First posted on arXiv 3 Jan 2024.

## Builds on (most cited first, 7 of 7)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [Bayesian Poisson Tucker Decomposition for Learning the Structure of International Relations](https://mlsanity.com/paper/1606.01855/) (2016)
- [Optimal spectral transportation with application to music transcription](https://mlsanity.com/paper/1609.09799/) (2016)
- [SWIFT: Scalable Wasserstein Factorization for Sparse Nonnegative Tensors](https://mlsanity.com/paper/2010.04081/) (2020)
- [Using Low-rank Representation of Abundance Maps and Nonnegative Tensor Factorization for Hyperspectral Nonlinear Unmixing](https://mlsanity.com/paper/2103.16204/) (2021)
- [A unified framework for non-negative matrix and tensor factorisations with a smoothed Wasserstein loss](https://mlsanity.com/paper/2104.01708/) (2021)

## Abstract (arXiv)

Nonnegative tensor factorization (NTF) has become an important tool for feature extraction and part-based representation with preserved intrinsic structure information from nonnegative high-order data. However, the original NTF methods utilize Euclidean or Kullback-Leibler divergence as the loss function which treats each feature equally leading to the neglect of the side-information of features. To utilize correlation information of features and manifold information of samples, we introduce Wasserstein manifold nonnegative tensor factorization (WMNTF), which minimizes the Wasserstein distance between the distribution of input tensorial data and the distribution of reconstruction. Although some researches about Wasserstein distance have been proposed in nonnegative matrix factorization (NMF), they ignore the spatial structure information of higher-order data. We use Wasserstein distance (a.k.a Earth Mover's distance or Optimal Transport distance) as a metric and add a graph regularizer to a latent factor. Experimental results demonstrate the effectiveness of the proposed method compared with other NMF and NTF methods.