# Deep Clustering with a Constraint for Topological Invariance based on Symmetric InfoNCE

arXiv: https://arxiv.org/abs/2303.03036 · HTML: https://mlsanity.com/paper/2303.03036/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 87 references that are in the map.
- First posted on arXiv 6 Mar 2023.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Self-labelling via simultaneous clustering and representation learning](https://mlsanity.com/paper/1911.05371/) (2019)
- [Invariant Information Clustering for Unsupervised Image Classification and Segmentation](https://mlsanity.com/paper/1807.06653/) (2018)
- [SCAN: Learning to Classify Images without Labels](https://mlsanity.com/paper/2005.12320/) (2020)
- [On Mutual Information Maximization for Representation Learning](https://mlsanity.com/paper/1907.13625/) (2019)
- [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)
- [Joint Unsupervised Learning of Deep Representations and Image Clusters](https://mlsanity.com/paper/1604.03628/) (2016)
- [Learning Discrete Representations via Information Maximizing Self-Augmented Training](https://mlsanity.com/paper/1702.08720/) (2017)
- [Unsupervised and Semi-supervised Learning with Categorical Generative Adversarial Networks](https://mlsanity.com/paper/1511.06390/) (2015)
- [SpectralNet: Spectral Clustering using Deep Neural Networks](https://mlsanity.com/paper/1801.01587/) (2018)
- [ClusterGAN : Latent Space Clustering in Generative Adversarial Networks](https://mlsanity.com/paper/1809.03627/) (2018)
- [N2D: (Not Too) Deep Clustering via Clustering the Local Manifold of an Autoencoded Embedding](https://mlsanity.com/paper/1908.05968/) (2019)
- [Deep Transformation-Invariant Clustering](https://mlsanity.com/paper/2006.11132/) (2020)
- [Connecting Language and Vision for Natural Language-Based Vehicle Retrieval](https://mlsanity.com/paper/2105.14897/) (2021)
- [Minimax-optimal semi-supervised regression on unknown manifolds](https://mlsanity.com/paper/1611.02221/) (2016)
- [Deep Learning with Nonparametric Clustering](https://mlsanity.com/paper/1501.03084/) (2015)
- [Generalized Clustering by Learning to Optimize Expected Normalized Cuts](https://mlsanity.com/paper/1910.07623/) (2019)

## Built on by (most cited first, 5 of 5)

- [Weighted Point Set Embedding for Multimodal Contrastive Learning Toward Optimal Similarity Metric](https://mlsanity.com/paper/2404.19228/) (2024)
- [Zero-Flow Encoders](https://mlsanity.com/paper/2602.00797/) (2026)
- [Theoretical Refinement of CLIP by Utilizing Linear Structure of Optimal Similarity](https://mlsanity.com/paper/2510.15508/) (2025)
- [Graph of Agents: Principled Long Context Modeling by Emergent Multi-Agent Collaboration](https://mlsanity.com/paper/2509.21848/) (2025)
- [SONA: Learning Conditional, Unconditional, and Mismatching-Aware Discriminator](https://mlsanity.com/paper/2510.04576/) (2025)

## Abstract (arXiv)

We consider the scenario of deep clustering, in which the available prior knowledge is limited. In this scenario, few existing state-of-the-art deep clustering methods can perform well for both non-complex topology and complex topology datasets. To address the problem, we propose a constraint utilizing symmetric InfoNCE, which helps an objective of deep clustering method in the scenario train the model so as to be efficient for not only non-complex topology but also complex topology datasets. Additionally, we provide several theoretical explanations of the reason why the constraint can enhances performance of deep clustering methods. To confirm the effectiveness of the proposed constraint, we introduce a deep clustering method named MIST, which is a combination of an existing deep clustering method and our constraint. Our numerical experiments via MIST demonstrate that the constraint is effective. In addition, MIST outperforms other state-of-the-art deep clustering methods for most of the commonly used ten benchmark datasets.