# Deep Spectral Clustering via Joint Spectral Embedding and Kmeans

arXiv: https://arxiv.org/abs/2412.11080 · HTML: https://mlsanity.com/paper/2412.11080/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 15 Dec 2024.

## Builds on (most cited first, 13 of 13)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Joint Unsupervised Learning of Deep Representations and Image Clusters](https://mlsanity.com/paper/1604.03628/) (2016)
- [Deep Clustering via Joint Convolutional Autoencoder Embedding and Relative Entropy Minimization](https://mlsanity.com/paper/1704.06327/) (2017)
- [SpectralNet: Spectral Clustering using Deep Neural Networks](https://mlsanity.com/paper/1801.01587/) (2018)
- [A Comprehensive Survey on Deep Clustering: Taxonomy, Challenges, and Future Directions](https://mlsanity.com/paper/2206.07579/) (2022)
- [ClusterLLM: Large Language Models as a Guide for Text Clustering](https://mlsanity.com/paper/2305.14871/) (2023)
- [Image Clustering Conditioned on Text Criteria](https://mlsanity.com/paper/2310.18297/) (2023)
- [Learning a Self-Expressive Network for Subspace Clustering](https://mlsanity.com/paper/2110.04318/) (2021)
- [Deep Embedded K-Means Clustering](https://mlsanity.com/paper/2109.15149/) (2021)
- [Spectral Clustering via the Power Method -- Provably](https://mlsanity.com/paper/1311.2854/) (2013)
- [Deep Clustering With Consensus Representations](https://mlsanity.com/paper/2210.07063/) (2022)

## Built on by (most cited first, 4 of 4)

- [On the Provable Importance of Gradients for Language-Assisted Image Clustering](https://mlsanity.com/paper/2510.16335/) (2025)
- [Bootstrap Deep Spectral Clustering with Optimal Transport](https://mlsanity.com/paper/2508.04200/) (2025)
- [Delving into Spectral Clustering with Vision-Language Representations](https://mlsanity.com/paper/2602.09586/) (2026)
- [Federated Multi-Task Clustering](https://mlsanity.com/paper/2512.22897/) (2025)

## Abstract (arXiv)

Spectral clustering is a popular clustering method. It first maps data into the spectral embedding space and then uses Kmeans to find clusters. However, the two decoupled steps prohibit joint optimization for the optimal solution. In addition, it needs to construct the similarity graph for samples, which suffers from the curse of dimensionality when the data are high-dimensional. To address these two challenges, we introduce Deep Spectral Clustering (DSC), which consists of two main modules: the spectral embedding module and the greedy Kmeans module. The former module learns to efficiently embed raw samples into the spectral embedding space using deep neural networks and power iteration. The latter module improves the cluster structures of Kmeans on the learned spectral embeddings by a greedy optimization strategy, which iteratively reveals the direction of the worst cluster structures and optimizes embeddings in this direction. To jointly optimize spectral embeddings and clustering, we seamlessly integrate the two modules and optimize them in an end-to-end manner. Experimental results on seven real-world datasets demonstrate that DSC achieves state-of-the-art clustering performance.