# Bootstrap Deep Spectral Clustering with Optimal Transport

arXiv: https://arxiv.org/abs/2508.04200 · HTML: https://mlsanity.com/paper/2508.04200/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 109 references that are in the map.
- First posted on arXiv 6 Aug 2025.

## Builds on (most cited first, 30 of 45)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Deep Clustering for Unsupervised Learning of Visual Features](https://mlsanity.com/paper/1807.05520/) (2018)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Self-labelling via simultaneous clustering and representation learning](https://mlsanity.com/paper/1911.05371/) (2019)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [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)
- [Contrastive Clustering](https://mlsanity.com/paper/2009.09687/) (2020)
- [Towards K-means-friendly Spaces: Simultaneous Deep Learning and Clustering](https://mlsanity.com/paper/1610.04794/) (2016)
- [Joint Unsupervised Learning of Deep Representations and Image Clusters](https://mlsanity.com/paper/1604.03628/) (2016)
- [OTA: Optimal Transport Assignment for Object Detection](https://mlsanity.com/paper/2103.14259/) (2021)
- [Deep Clustering via Joint Convolutional Autoencoder Embedding and Relative Entropy Minimization](https://mlsanity.com/paper/1704.06327/) (2017)
- [Online Deep Clustering for Unsupervised Representation Learning](https://mlsanity.com/paper/2006.10645/) (2020)
- [Deep Subspace Clustering Networks](https://mlsanity.com/paper/1709.02508/) (2017)
- [SpectralNet: Spectral Clustering using Deep Neural Networks](https://mlsanity.com/paper/1801.01587/) (2018)
- [Deep Comprehensive Correlation Mining for Image Clustering](https://mlsanity.com/paper/1904.06925/) (2019)
- [Large Language Models Enable Few-Shot Clustering](https://mlsanity.com/paper/2307.00524/) (2023)
- [Deep Spectral Clustering using Dual Autoencoder Network](https://mlsanity.com/paper/1904.13113/) (2019)
- [ClusterLLM: Large Language Models as a Guide for Text Clustering](https://mlsanity.com/paper/2305.14871/) (2023)
- [Clustering-friendly Representation Learning via Instance Discrimination and Feature Decorrelation](https://mlsanity.com/paper/2106.00131/) (2021)

## Built on by (most cited first, 2 of 2)

- [On the Provable Importance of Gradients for Language-Assisted Image Clustering](https://mlsanity.com/paper/2510.16335/) (2025)
- [Delving into Spectral Clustering with Vision-Language Representations](https://mlsanity.com/paper/2602.09586/) (2026)

## Abstract (arXiv)

Spectral clustering is a leading clustering method. Two of its major shortcomings are the disjoint optimization process and the limited representation capacity. To address these issues, we propose a deep spectral clustering model (named BootSC), which jointly learns all stages of spectral clustering -- affinity matrix construction, spectral embedding, and k-means clustering -- using a single network in an end-to-end manner. BootSC leverages effective and efficient optimal-transport-derived supervision to bootstrap the affinity matrix and the cluster assignment matrix. Moreover, a semantically-consistent orthogonal re-parameterization technique is introduced to orthogonalize spectral embeddings, significantly enhancing the discrimination capability. Experimental results indicate that BootSC achieves state-of-the-art clustering performance. For example, it accomplishes a notable 16% NMI improvement over the runner-up method on the challenging ImageNet-Dogs dataset. Our code is available at https://github.com/spdj2271/BootSC.