# Joint Optimization of an Autoencoder for Clustering and Embedding

arXiv: https://arxiv.org/abs/2012.03740 · HTML: https://mlsanity.com/paper/2012.03740/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2020.

## Built on by (most cited first, 10 of 10)

- [Deep Clustering of Tabular Data by Weighted Gaussian Distribution Learning](https://mlsanity.com/paper/2301.00802/) (2023)
- [Effectiveness of Deep Image Embedding Clustering Methods on Tabular Data](https://mlsanity.com/paper/2212.14111/) (2022)
- [Mining Electronic Health Records to Investigate Effectiveness of Ensemble Deep Clustering](https://mlsanity.com/paper/2604.07085/) (2026)
- [Sanitized Clustering against Confounding Bias](https://mlsanity.com/paper/2311.01252/) (2023)
- [Supercm: Revisiting Clustering for Semi-Supervised Learning](https://mlsanity.com/paper/2506.23824/) (2025)
- [Simple and Scalable Algorithms for Cluster-Aware Precision Medicine](https://mlsanity.com/paper/2211.16553/) (2022)
- [SuperCM: Improving Semi-Supervised Learning and Domain Adaptation through differentiable clustering](https://mlsanity.com/paper/2507.13779/) (2025)
- [From Points to Spheres: A Geometric Reinterpretation of Variational Autoencoders](https://mlsanity.com/paper/2507.17255/) (2025)
- [ε-Seg: Sparsely Supervised Semantic Segmentation of Microscopy Data](https://mlsanity.com/paper/2510.18637/) (2025)
- [Ensemble of Unsupervised Deep Learning for Clustering Imbalanced Tabular Data](https://mlsanity.com/paper/2608.00346/) (2026)

## Abstract (arXiv)

Deep embedded clustering has become a dominating approach to unsupervised categorization of objects with deep neural networks. The optimization of the most popular methods alternates between the training of a deep autoencoder and a k-means clustering of the autoencoder's embedding. The diachronic setting, however, prevents the former to benefit from valuable information acquired by the latter. In this paper, we present an alternative where the autoencoder and the clustering are learned simultaneously. This is achieved by providing novel theoretical insight, where we show that the objective function of a certain class of Gaussian mixture models (GMMs) can naturally be rephrased as the loss function of a one-hidden layer autoencoder thus inheriting the built-in clustering capabilities of the GMM. That simple neural network, referred to as the clustering module, can be integrated into a deep autoencoder resulting in a deep clustering model able to jointly learn a clustering and an embedding. Experiments confirm the equivalence between the clustering module and Gaussian mixture models. Further evaluations affirm the empirical relevance of our deep architecture as it outperforms related baselines on several data sets.