# Deep Embedded K-Means Clustering

arXiv: https://arxiv.org/abs/2109.15149 · HTML: https://mlsanity.com/paper/2109.15149/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 48 references that are in the map.
- First posted on arXiv 30 Sep 2021.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [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)
- [Deep Clustering via Joint Convolutional Autoencoder Embedding and Relative Entropy Minimization](https://mlsanity.com/paper/1704.06327/) (2017)
- [Deep k-Means: Jointly clustering with k-Means and learning representations](https://mlsanity.com/paper/1806.10069/) (2018)
- [Discriminatively Boosted Image Clustering with Fully Convolutional Auto-Encoders](https://mlsanity.com/paper/1703.07980/) (2017)
- [Deep Continuous Clustering](https://mlsanity.com/paper/1803.01449/) (2018)

## Built on by (most cited first, 12 of 12)

- [On the Provable Importance of Gradients for Language-Assisted Image Clustering](https://mlsanity.com/paper/2510.16335/) (2025)
- [Deep Clustering Using the Soft Silhouette Score: Towards Compact and Well-Separated Clusters](https://mlsanity.com/paper/2402.00608/) (2024)
- [Deep Spectral Clustering via Joint Spectral Embedding and Kmeans](https://mlsanity.com/paper/2412.11080/) (2024)
- [UniForCE: The Unimodality Forest Method for Clustering and Estimation of the Number of Clusters](https://mlsanity.com/paper/2312.11323/) (2023)
- [A Fresh Look at Generalized Category Discovery through Non-negative Matrix Factorization](https://mlsanity.com/paper/2410.21807/) (2024)
- [Bootstrap Deep Spectral Clustering with Optimal Transport](https://mlsanity.com/paper/2508.04200/) (2025)
- [Deep Clustering with Associative Memories](https://mlsanity.com/paper/2601.00963/) (2026)
- [Delving into Spectral Clustering with Vision-Language Representations](https://mlsanity.com/paper/2602.09586/) (2026)
- [Scalable Context-Preserving Model-Aware Deep Clustering for Hyperspectral Images](https://mlsanity.com/paper/2506.11377/) (2025)
- [Joint Superpixel and Self-Representation Learning for Scalable Hyperspectral Image Clustering](https://mlsanity.com/paper/2509.24027/) (2025)
- [A Neuro-Fuzzy System for Interpretable Long-Term Stock Market Forecasting](https://mlsanity.com/paper/2510.00960/) (2025)
- [NSVQ: Mitigating Codebook Collapse by Stabilizing Encoder Drift in Vector Quantization](https://mlsanity.com/paper/2606.11363/) (2026)

## Abstract (arXiv)

Recently, deep clustering methods have gained momentum because of the high representational power of deep neural networks (DNNs) such as autoencoder. The key idea is that representation learning and clustering can reinforce each other: Good representations lead to good clustering while good clustering provides good supervisory signals to representation learning. Critical questions include: 1) How to optimize representation learning and clustering? 2) Should the reconstruction loss of autoencoder be considered always? In this paper, we propose DEKM (for Deep Embedded K-Means) to answer these two questions. Since the embedding space generated by autoencoder may have no obvious cluster structures, we propose to further transform the embedding space to a new space that reveals the cluster-structure information. This is achieved by an orthonormal transformation matrix, which contains the eigenvectors of the within-class scatter matrix of K-means. The eigenvalues indicate the importance of the eigenvectors' contributions to the cluster-structure information in the new space. Our goal is to increase the cluster-structure information. To this end, we discard the decoder and propose a greedy method to optimize the representation. Representation learning and clustering are alternately optimized by DEKM. Experimental results on the real-world datasets demonstrate that DEKM achieves state-of-the-art performance.