# Differentiable Deep Clustering with Cluster Size Constraints

arXiv: https://arxiv.org/abs/1910.09036 · HTML: https://mlsanity.com/paper/1910.09036/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2019.

## Built on by (most cited first, 22 of 22)

- [Effective Neural Topic Modeling with Embedding Clustering Regularization](https://mlsanity.com/paper/2306.04217/) (2023)
- [Orchestra: Unsupervised Federated Learning via Globally Consistent Clustering](https://mlsanity.com/paper/2205.11506/) (2022)
- [FASTopic: Pretrained Transformer is a Fast, Adaptive, Stable, and Transferable Topic Model](https://mlsanity.com/paper/2405.17978/) (2024)
- [Sparsity-Constrained Optimal Transport](https://mlsanity.com/paper/2209.15466/) (2022)
- [On the Affinity, Rationality, and Diversity of Hierarchical Topic Modeling](https://mlsanity.com/paper/2401.14113/) (2024)
- [Rethinking Initialization of the Sinkhorn Algorithm](https://mlsanity.com/paper/2206.07630/) (2022)
- [Differentiable Clustering with Perturbed Spanning Forests](https://mlsanity.com/paper/2305.16358/) (2023)
- [Combining pretrained CNN feature extractors to enhance clustering of complex natural images](https://mlsanity.com/paper/2101.02767/) (2021)
- [Towards Unbiased Training in Federated Open-world Semi-supervised Learning](https://mlsanity.com/paper/2305.00771/) (2023)
- [Learning crop type mapping from regional label proportions in large-scale SAR and optical imagery](https://mlsanity.com/paper/2208.11607/) (2022)
- [Federated Continual Novel Class Learning](https://mlsanity.com/paper/2312.13500/) (2023)
- [Solving a Special Type of Optimal Transport Problem by a Modified Hungarian Algorithm](https://mlsanity.com/paper/2210.16645/) (2022)
- [Enhancing Interpretable Object Abstraction via Clustering-based Slot Initialization](https://mlsanity.com/paper/2308.11369/) (2023)
- [Neural Capacitated Clustering](https://mlsanity.com/paper/2302.05134/) (2023)
- [Polytopic Autoencoders with Smooth Clustering for Reduced-order Modelling of Flows](https://mlsanity.com/paper/2401.10620/) (2024)
- [Differentiable Cost-Parameterized Monge Map Estimators](https://mlsanity.com/paper/2406.08399/) (2024)
- [Graph Cuts with Arbitrary Size Constraints Through Optimal Transport](https://mlsanity.com/paper/2402.04732/) (2024)
- [On Model-Based Clustering With Entropic Optimal Transport](https://mlsanity.com/paper/2605.03240/) (2026)
- [Few-Example Clustering via Contrastive Learning](https://mlsanity.com/paper/2207.04050/) (2022)
- [A Personalized Video-Based Hand Taxonomy: Application for Individuals with Spinal Cord Injury](https://mlsanity.com/paper/2403.18094/) (2024)
- [An Approach Towards Learning K-means-friendly Deep Latent Representation](https://mlsanity.com/paper/2411.19496/) (2024)
- [Consistency and inconsistency in k-means clustering](https://mlsanity.com/paper/2507.06226/) (2025)

## Abstract (arXiv)

Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as k-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data such as images. Learning a lower-dimensional embedding that can better reflect the geometry of the dataset is therefore instrumental for performance. We propose a new approach for this task where the embedding is performed by a differentiable model such as a deep neural network. By rewriting the k-means clustering algorithm as an optimal transport task, and adding an entropic regularization, we derive a fully differentiable loss function that can be minimized with respect to both the embedding parameters and the cluster parameters via stochastic gradient descent. We show that this new formulation generalizes a recently proposed state-of-the-art method based on soft-k-means by adding constraints on the cluster sizes. Empirical evaluations on image classification benchmarks suggest that compared to state-of-the-art methods, our optimal transport-based approach provide better unsupervised accuracy and does not require a pre-training phase.