# Exploring a Principled Framework for Deep Subspace Clustering

arXiv: https://arxiv.org/abs/2503.17288 · HTML: https://mlsanity.com/paper/2503.17288/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 98 references that are in the map.
- First posted on arXiv 21 Mar 2025.

## Builds on (most cited first, 30 of 54)

- [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)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [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)
- [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)
- [Implicit Regularization in Deep Matrix Factorization](https://mlsanity.com/paper/1905.13655/) (2019)
- [SCAN: Learning to Classify Images without Labels](https://mlsanity.com/paper/2005.12320/) (2020)
- [Implicit Regularization in Matrix Factorization](https://mlsanity.com/paper/1705.09280/) (2017)
- [Contrastive Clustering](https://mlsanity.com/paper/2009.09687/) (2020)
- [Joint Unsupervised Learning of Deep Representations and Image Clusters](https://mlsanity.com/paper/1604.03628/) (2016)
- [Learning Diverse and Discriminative Representations via the Principle of Maximal Coding Rate Reduction](https://mlsanity.com/paper/2006.08558/) (2020)
- [SPICE: Semantic Pseudo-labeling for Image Clustering](https://mlsanity.com/paper/2103.09382/) (2021)
- [Deep Subspace Clustering Networks](https://mlsanity.com/paper/1709.02508/) (2017)
- [Graph Contrastive Clustering](https://mlsanity.com/paper/2104.01429/) (2021)
- [Learning Representation for Clustering via Prototype Scattering and Positive Sampling](https://mlsanity.com/paper/2111.11821/) (2021)
- [Improving Unsupervised Image Clustering With Robust Learning](https://mlsanity.com/paper/2012.11150/) (2020)
- [Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit](https://mlsanity.com/paper/1507.01238/) (2015)
- [Robust and Efficient Subspace Segmentation via Least Squares Regression](https://mlsanity.com/paper/1404.6736/) (2014)
- [Neural Manifold Clustering and Embedding](https://mlsanity.com/paper/2201.10000/) (2022)
- [Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering](https://mlsanity.com/paper/1605.02633/) (2016)
- [Subspace Clustering by Block Diagonal Representation](https://mlsanity.com/paper/1805.09243/) (2018)
- [OL'E: Orthogonal Low-rank Embedding, A Plug and Play Geometric Loss for Deep Learning](https://mlsanity.com/paper/1712.01727/) (2017)

## Built on by (most cited first, 7 of 7)

- [Temporal Rate Reduction Clustering for Human Motion Segmentation](https://mlsanity.com/paper/2506.21249/) (2025)
- [Dimensionally Reduced Open-World Clustering: DROWCULA](https://mlsanity.com/paper/2509.07184/) (2025)
- [Subspace Clustering on Incomplete Data with Self-Supervised Contrastive Learning](https://mlsanity.com/paper/2602.00262/) (2026)
- [Language-Assisted Image Clustering Guided by Discriminative Relational Signals and Adaptive Semantic Centers](https://mlsanity.com/paper/2603.24275/) (2026)
- [Jointly Learning Structured Representations and Stabilized Affinity for Human Motion Segmentation](https://mlsanity.com/paper/2605.05753/) (2026)
- [Learning Deep Modality-Shared Self-Expressiveness for Image Clustering with Textual Information](https://mlsanity.com/paper/2608.08418/) (2026)
- [VLM4Cluster: Benchmarking Deep Clustering In the Era of Vision-Language Pre-training](https://mlsanity.com/paper/2609.36648/) (2026)

## Abstract (arXiv)

Subspace clustering is a classical unsupervised learning task, built on a basic assumption that high-dimensional data can be approximated by a union of subspaces (UoS). Nevertheless, the real-world data are often deviating from the UoS assumption. To address this challenge, state-of-the-art deep subspace clustering algorithms attempt to jointly learn UoS representations and self-expressive coefficients. However, the general framework of the existing algorithms suffers from a catastrophic feature collapse and lacks a theoretical guarantee to learn desired UoS representation. In this paper, we present a Principled fRamewOrk for Deep Subspace Clustering (PRO-DSC), which is designed to learn structured representations and self-expressive coefficients in a unified manner. Specifically, in PRO-DSC, we incorporate an effective regularization on the learned representations into the self-expressive model, prove that the regularized self-expressive model is able to prevent feature space collapse, and demonstrate that the learned optimal representations under certain condition lie on a union of orthogonal subspaces. Moreover, we provide a scalable and efficient approach to implement our PRO-DSC and conduct extensive experiments to verify our theoretical findings and demonstrate the superior performance of our proposed deep subspace clustering approach. The code is available at https://github.com/mengxianghan123/PRO-DSC.