# A Critique of Self-Expressive Deep Subspace Clustering

arXiv: https://arxiv.org/abs/2010.03697 · HTML: https://mlsanity.com/paper/2010.03697/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2020.

## Built on by (most cited first, 18 of 18)

- [Neural Manifold Clustering and Embedding](https://mlsanity.com/paper/2201.10000/) (2022)
- [Do Sparse Autoencoders Capture Concept Manifolds?](https://mlsanity.com/paper/2604.28119/) (2026)
- [Learning a Self-Expressive Network for Subspace Clustering](https://mlsanity.com/paper/2110.04318/) (2021)
- [Robust CUR Decomposition: Theory and Imaging Applications](https://mlsanity.com/paper/2101.05231/) (2021)
- [Learning segmentation from point trajectories](https://mlsanity.com/paper/2501.12392/) (2025)
- [Superpixel-based and Spatially-regularized Diffusion Learning for Unsupervised Hyperspectral Image Clustering](https://mlsanity.com/paper/2312.15447/) (2023)
- [Unsupervised Manifold Linearizing and Clustering](https://mlsanity.com/paper/2301.01805/) (2023)
- [Exploring a Principled Framework for Deep Subspace Clustering](https://mlsanity.com/paper/2503.17288/) (2025)
- [Unsupervised Diffusion and Volume Maximization-Based Clustering of Hyperspectral Images](https://mlsanity.com/paper/2203.09992/) (2022)
- [Adaptive Graph Convolutional Subspace Clustering](https://mlsanity.com/paper/2305.03414/) (2023)
- [Multilayer Graph Approach to Deep Subspace Clustering](https://mlsanity.com/paper/2401.17033/) (2024)
- [Temporal Rate Reduction Clustering for Human Motion Segmentation](https://mlsanity.com/paper/2506.21249/) (2025)
- [Beyond Linear Subspace Clustering: A Comparative Study of Nonlinear Manifold Clustering Algorithms](https://mlsanity.com/paper/2103.10656/) (2021)
- [Federated Deep Subspace Clustering](https://mlsanity.com/paper/2501.00230/) (2024)
- [Label-independent hyperparameter-free self-supervised single-view deep subspace clustering](https://mlsanity.com/paper/2504.18179/) (2025)
- [Normalizing Flow to Augmented Posterior: Conditional Density Estimation with Interpretable Dimension Reduction for High Dimensional Data](https://mlsanity.com/paper/2507.04216/) (2025)
- [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)

## Abstract (arXiv)

Subspace clustering is an unsupervised clustering technique designed to cluster data that is supported on a union of linear subspaces, with each subspace defining a cluster with dimension lower than the ambient space. Many existing formulations for this problem are based on exploiting the self-expressive property of linear subspaces, where any point within a subspace can be represented as linear combination of other points within the subspace. To extend this approach to data supported on a union of non-linear manifolds, numerous studies have proposed learning an embedding of the original data using a neural network which is regularized by a self-expressive loss function on the data in the embedded space to encourage a union of linear subspaces prior on the data in the embedded space. Here we show that there are a number of potential flaws with this approach which have not been adequately addressed in prior work. In particular, we show the model formulation is often ill-posed in that it can lead to a degenerate embedding of the data, which need not correspond to a union of subspaces at all and is poorly suited for clustering. We validate our theoretical results experimentally and also repeat prior experiments reported in the literature, where we conclude that a significant portion of the previously claimed performance benefits can be attributed to an ad-hoc post processing step rather than the deep subspace clustering model.