# Deep Clustering via Probabilistic Ratio-Cut Optimization

arXiv: https://arxiv.org/abs/2502.03405 · HTML: https://mlsanity.com/paper/2502.03405/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 33 references that are in the map.
- First posted on arXiv 5 Feb 2025.

## Builds on (most cited first, 14 of 14)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [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)
- [Hierarchical Deep Reinforcement Learning: Integrating Temporal Abstraction and Intrinsic Motivation](https://mlsanity.com/paper/1604.06057/) (2016)
- [Contrastive Clustering](https://mlsanity.com/paper/2009.09687/) (2020)
- [Variational Deep Embedding: An Unsupervised and Generative Approach to Clustering](https://mlsanity.com/paper/1611.05148/) (2016)
- [Solo-learn: A Library of Self-supervised Methods for Visual Representation Learning](https://mlsanity.com/paper/2108.01775/) (2021)
- [A Laplacian Framework for Option Discovery in Reinforcement Learning](https://mlsanity.com/paper/1703.00956/) (2017)
- [SpectralNet: Spectral Clustering using Deep Neural Networks](https://mlsanity.com/paper/1801.01587/) (2018)
- [Eigenoption Discovery through the Deep Successor Representation](https://mlsanity.com/paper/1710.11089/) (2017)
- [Spectral Inference Networks: Unifying Deep and Spectral Learning](https://mlsanity.com/paper/1806.02215/) (2018)
- [Let Go of Your Labels with Unsupervised Transfer](https://mlsanity.com/paper/2406.07236/) (2024)
- [All4One: Symbiotic Neighbour Contrastive Learning via Self-Attention and Redundancy Reduction](https://mlsanity.com/paper/2303.09417/) (2023)
- [The VampPrior Mixture Model](https://mlsanity.com/paper/2402.04412/) (2024)

## Built on by (most cited first, 1 of 1)

- [Dimensionally Reduced Open-World Clustering: DROWCULA](https://mlsanity.com/paper/2509.07184/) (2025)

## Abstract (arXiv)

We propose a novel approach for optimizing the graph ratio-cut by modeling the binary assignments as random variables. We provide an upper bound on the expected ratio-cut, as well as an unbiased estimate of its gradient, to learn the parameters of the assignment variables in an online setting. The clustering resulting from our probabilistic approach (PRCut) outperforms the Rayleigh quotient relaxation of the combinatorial problem, its online learning extensions, and several widely used methods. We demonstrate that the PRCut clustering closely aligns with the similarity measure and can perform as well as a supervised classifier when label-based similarities are provided. This novel approach can leverage out-of-the-box self-supervised representations to achieve competitive performance and serve as an evaluation method for the quality of these representations.