# Learning a Self-Expressive Network for Subspace Clustering

arXiv: https://arxiv.org/abs/2110.04318 · HTML: https://mlsanity.com/paper/2110.04318/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 91 references that are in the map.
- First posted on arXiv 8 Oct 2021.

## Builds on (most cited first, 30 of 40)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (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)
- [Learning Diverse and Discriminative Representations via the Principle of Maximal Coding Rate Reduction](https://mlsanity.com/paper/2006.08558/) (2020)
- [Deep Clustering via Joint Convolutional Autoencoder Embedding and Relative Entropy Minimization](https://mlsanity.com/paper/1704.06327/) (2017)
- [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)
- [ClusterGAN : Latent Space Clustering in Generative Adversarial Networks](https://mlsanity.com/paper/1809.03627/) (2018)
- [Deep Spectral Clustering using Dual Autoencoder Network](https://mlsanity.com/paper/1904.13113/) (2019)
- [Robust and Efficient Subspace Segmentation via Least Squares Regression](https://mlsanity.com/paper/1404.6736/) (2014)
- [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)
- [Sparse Representation-based Open Set Recognition](https://mlsanity.com/paper/1705.02431/) (2017)
- [Self-Supervised Convolutional Subspace Clustering Network](https://mlsanity.com/paper/1905.00149/) (2019)
- [Structured Sparse Subspace Clustering: A Joint Affinity Learning and Subspace Clustering Framework](https://mlsanity.com/paper/1610.05211/) (2016)
- [Robust subspace clustering](https://mlsanity.com/paper/1301.2603/) (2013)
- [Neural Collaborative Subspace Clustering](https://mlsanity.com/paper/1904.10596/) (2019)
- [Noisy Sparse Subspace Clustering](https://mlsanity.com/paper/1309.1233/) (2013)
- [Provable Self-Representation Based Outlier Detection in a Union of Subspaces](https://mlsanity.com/paper/1704.03925/) (2017)
- [A Critique of Self-Expressive Deep Subspace Clustering](https://mlsanity.com/paper/2010.03697/) (2020)
- [Stochastic Sparse Subspace Clustering](https://mlsanity.com/paper/2005.01449/) (2020)
- [Analysis and Design of Convolutional Networks via Hierarchical Tensor Decompositions](https://mlsanity.com/paper/1705.02302/) (2017)
- [On Geometric Analysis of Affine Sparse Subspace Clustering](https://mlsanity.com/paper/1808.05965/) (2018)
- [Greedy Feature Selection for Subspace Clustering](https://mlsanity.com/paper/1303.4778/) (2013)

## Built on by (most cited first, 24 of 24)

- [A Comprehensive Survey on Deep Clustering: Taxonomy, Challenges, and Future Directions](https://mlsanity.com/paper/2206.07579/) (2022)
- [Neural Manifold Clustering and Embedding](https://mlsanity.com/paper/2201.10000/) (2022)
- [Unsupervised Manifold Linearizing and Clustering](https://mlsanity.com/paper/2301.01805/) (2023)
- [Adversarial Examples Might be Avoidable: The Role of Data Concentration in Adversarial Robustness](https://mlsanity.com/paper/2309.16096/) (2023)
- [Exploring a Principled Framework for Deep Subspace Clustering](https://mlsanity.com/paper/2503.17288/) (2025)
- [Rotation and Translation Invariant Representation Learning with Implicit Neural Representations](https://mlsanity.com/paper/2304.13995/) (2023)
- [Deep Spectral Clustering via Joint Spectral Embedding and Kmeans](https://mlsanity.com/paper/2412.11080/) (2024)
- [Unsupervised Deep Discriminant Analysis Based Clustering](https://mlsanity.com/paper/2206.04686/) (2022)
- [Neural Normalized Cut: A Differential and Generalizable Approach for Spectral Clustering](https://mlsanity.com/paper/2503.09260/) (2025)
- [Delving into Spectral Clustering with Vision-Language Representations](https://mlsanity.com/paper/2602.09586/) (2026)
- [PMSSC: Parallelizable multi-subset based self-expressive model for subspace clustering](https://mlsanity.com/paper/2111.12232/) (2021)
- [Deep Structure and Attention Aware Subspace Clustering](https://mlsanity.com/paper/2312.15577/) (2023)
- [Contrastive Learning Subspace for Text Clustering](https://mlsanity.com/paper/2408.14119/) (2024)
- [Temporal Rate Reduction Clustering for Human Motion Segmentation](https://mlsanity.com/paper/2506.21249/) (2025)
- [Learning Deep Representation with Energy-Based Self-Expressiveness for Subspace Clustering](https://mlsanity.com/paper/2110.15037/) (2021)
- [Inv-SENnet: Invariant Self Expression Network for clustering under biased data](https://mlsanity.com/paper/2211.06780/) (2022)
- [On Interpretable Approaches to Cluster, Classify and Represent Multi-Subspace Data via Minimum Lossy Coding Length based on Rate-Distortion Theory](https://mlsanity.com/paper/2302.10383/) (2023)
- [Learning Structure Aware Deep Spectral Embedding](https://mlsanity.com/paper/2305.08215/) (2023)
- [Efficient and Effective Deep Multi-view Subspace Clustering](https://mlsanity.com/paper/2310.09718/) (2023)
- [Beyond Binary Classification: A Semi-supervised Approach to Generalized AI-generated Image Detection](https://mlsanity.com/paper/2511.19499/) (2025)
- [Subspace Clustering on Incomplete Data with Self-Supervised Contrastive Learning](https://mlsanity.com/paper/2602.00262/) (2026)
- [CASC: Causal Adversarial Subspace Clustering for Multivariate Spatiotemporal Data](https://mlsanity.com/paper/2607.21088/) (2026)
- [Learning Deep Modality-Shared Self-Expressiveness for Image Clustering with Textual Information](https://mlsanity.com/paper/2608.08418/) (2026)
- [Adversarial Consistency-Guided Representation Learning for Multi-view Clustering](https://mlsanity.com/paper/2609.35212/) (2026)

## Abstract (arXiv)

State-of-the-art subspace clustering methods are based on self-expressive model, which represents each data point as a linear combination of other data points. However, such methods are designed for a finite sample dataset and lack the ability to generalize to out-of-sample data. Moreover, since the number of self-expressive coefficients grows quadratically with the number of data points, their ability to handle large-scale datasets is often limited. In this paper, we propose a novel framework for subspace clustering, termed Self-Expressive Network (SENet), which employs a properly designed neural network to learn a self-expressive representation of the data. We show that our SENet can not only learn the self-expressive coefficients with desired properties on the training data, but also handle out-of-sample data. Besides, we show that SENet can also be leveraged to perform subspace clustering on large-scale datasets. Extensive experiments conducted on synthetic data and real world benchmark data validate the effectiveness of the proposed method. In particular, SENet yields highly competitive performance on MNIST, Fashion MNIST and Extended MNIST and state-of-the-art performance on CIFAR-10. The code is available at https://github.com/zhangsz1998/Self-Expressive-Network.