# SeGMA: Semi-Supervised Gaussian Mixture Auto-Encoder

arXiv: https://arxiv.org/abs/1906.09333 · HTML: https://mlsanity.com/paper/1906.09333/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2019.

## Built on by (most cited first, 7 of 7)

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- [Cramer Type Distances for Learning Gaussian Mixture Models by Gradient Descent](https://mlsanity.com/paper/2307.06753/) (2023)
- [Schema matching using Gaussian mixture models with Wasserstein distance](https://mlsanity.com/paper/2111.14244/) (2021)
- [A generative recommender system with GMM prior for cancer drug generation and sensitivity prediction](https://mlsanity.com/paper/2206.03555/) (2022)
- [ε-Seg: Sparsely Supervised Semantic Segmentation of Microscopy Data](https://mlsanity.com/paper/2510.18637/) (2025)
- [Semi-Supervised Learning under General Causal Models](https://mlsanity.com/paper/2510.22567/) (2025)

## Abstract (arXiv)

We propose a semi-supervised generative model, SeGMA, which learns a joint probability distribution of data and their classes and which is implemented in a typical Wasserstein auto-encoder framework. We choose a mixture of Gaussians as a target distribution in latent space, which provides a natural splitting of data into clusters. To connect Gaussian components with correct classes, we use a small amount of labeled data and a Gaussian classifier induced by the target distribution. SeGMA is optimized efficiently due to the use of Cramer-Wold distance as a maximum mean discrepancy penalty, which yields a closed-form expression for a mixture of spherical Gaussian components and thus obviates the need of sampling. While SeGMA preserves all properties of its semi-supervised predecessors and achieves at least as good generative performance on standard benchmark data sets, it presents additional features: (a) interpolation between any pair of points in the latent space produces realistically-looking samples; (b) combining the interpolation property with disentangled class and style variables, SeGMA is able to perform a continuous style transfer from one class to another; (c) it is possible to change the intensity of class characteristics in a data point by moving the latent representation of the data point away from specific Gaussian components.