# Schema matching using Gaussian mixture models with Wasserstein distance

arXiv: https://arxiv.org/abs/2111.14244 · HTML: https://mlsanity.com/paper/2111.14244/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 9 references that are in the map.
- First posted on arXiv 28 Nov 2021.

## Builds on (most cited first, 5 of 5)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [A Wasserstein-type distance in the space of Gaussian Mixture Models](https://mlsanity.com/paper/1907.05254/) (2019)
- [SeGMA: Semi-Supervised Gaussian Mixture Auto-Encoder](https://mlsanity.com/paper/1906.09333/) (2019)
- [Improved Deep Spectral Convolution Network For Hyperspectral Unmixing With Multinomial Mixture Kernel and Endmember Uncertainty](https://mlsanity.com/paper/1808.01104/) (2018)
- [Gaussian mixture models with Wasserstein distance](https://mlsanity.com/paper/1806.04465/) (2018)

## Abstract (arXiv)

Gaussian mixture models find their place as a powerful tool, mostly in the clustering problem, but with proper preparation also in feature extraction, pattern recognition, image segmentation and in general machine learning. When faced with the problem of schema matching, different mixture models computed on different pieces of data can maintain crucial information about the structure of the dataset. In order to measure or compare results from mixture models, the Wasserstein distance can be very useful, however it is not easy to calculate for mixture distributions. In this paper we derive one of possible approximations for the Wasserstein distance between Gaussian mixture models and reduce it to linear problem. Furthermore, application examples concerning real world data are shown.