# Deep Conditional Gaussian Mixture Model for Constrained Clustering

arXiv: https://arxiv.org/abs/2106.06385 · HTML: https://mlsanity.com/paper/2106.06385/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 42 references that are in the map.
- First posted on arXiv 11 Jun 2021.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [Age Progression/Regression by Conditional Adversarial Autoencoder](https://mlsanity.com/paper/1702.08423/) (2017)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [Variational Deep Embedding: An Unsupervised and Generative Approach to Clustering](https://mlsanity.com/paper/1611.05148/) (2016)
- [A Framework for Deep Constrained Clustering -- Algorithms and Advances](https://mlsanity.com/paper/1901.10061/) (2019)
- [Neural network-based clustering using pairwise constraints](https://mlsanity.com/paper/1511.06321/) (2015)
- [Learning Latent Superstructures in Variational Autoencoders for Deep Multidimensional Clustering](https://mlsanity.com/paper/1803.05206/) (2018)
- [A Classification-Based Approach to Semi-Supervised Clustering with Pairwise Constraints](https://mlsanity.com/paper/2001.06720/) (2020)
- [Semi-Supervised Clustering with Neural Networks](https://mlsanity.com/paper/1806.01547/) (2018)
- [Semi-crowdsourced Clustering with Deep Generative Models](https://mlsanity.com/paper/1810.11971/) (2018)
- [Correlated Variational Auto-Encoders](https://mlsanity.com/paper/1905.05335/) (2019)
- [Deep Transductive Semi-supervised Maximum Margin Clustering](https://mlsanity.com/paper/1501.06237/) (2015)
- [DPSOM: Deep Probabilistic Clustering with Self-Organizing Maps](https://mlsanity.com/paper/1910.01590/) (2019)

## Built on by (most cited first, 14 of 14)

- [ClusterLLM: Large Language Models as a Guide for Text Clustering](https://mlsanity.com/paper/2305.14871/) (2023)
- [Tree Variational Autoencoders](https://mlsanity.com/paper/2306.08984/) (2023)
- [Unsupervised Tissue Segmentation via Deep Constrained Gaussian Network](https://mlsanity.com/paper/2208.02912/) (2022)
- [Learning Group Importance using the Differentiable Hypergeometric Distribution](https://mlsanity.com/paper/2203.01629/) (2022)
- [Variational Classification](https://mlsanity.com/paper/2305.10406/) (2023)
- [Deep Clustering with Incomplete Noisy Pairwise Annotations: A Geometric Regularization Approach](https://mlsanity.com/paper/2305.19391/) (2023)
- [Personalized Clustering via Targeted Representation Learning](https://mlsanity.com/paper/2412.13690/) (2024)
- [Differentiable Random Partition Models](https://mlsanity.com/paper/2305.16841/) (2023)
- [Transformers as Unsupervised Learning Algorithms: A study on Gaussian Mixtures](https://mlsanity.com/paper/2505.11918/) (2025)
- [Neural Capacitated Clustering](https://mlsanity.com/paper/2302.05134/) (2023)
- [Angular Constraint Embedding via SpherePair Loss for Constrained Clustering](https://mlsanity.com/paper/2510.06907/) (2025)
- [Task-Prior Conditional Variational Auto-Encoder for Few-Shot Image Classification](https://mlsanity.com/paper/2205.15014/) (2022)
- [Oracle-guided Contrastive Clustering](https://mlsanity.com/paper/2211.00409/) (2022)
- [Uncertainty-Aware Probabilistic Constrained Clustering from Entangled Pairwise Supervision](https://mlsanity.com/paper/2608.12027/) (2026)

## Abstract (arXiv)

Constrained clustering has gained significant attention in the field of machine learning as it can leverage prior information on a growing amount of only partially labeled data. Following recent advances in deep generative models, we propose a novel framework for constrained clustering that is intuitive, interpretable, and can be trained efficiently in the framework of stochastic gradient variational inference. By explicitly integrating domain knowledge in the form of probabilistic relations, our proposed model (DC-GMM) uncovers the underlying distribution of data conditioned on prior clustering preferences, expressed as pairwise constraints. These constraints guide the clustering process towards a desirable partition of the data by indicating which samples should or should not belong to the same cluster. We provide extensive experiments to demonstrate that DC-GMM shows superior clustering performances and robustness compared to state-of-the-art deep constrained clustering methods on a wide range of data sets. We further demonstrate the usefulness of our approach on two challenging real-world applications.