# Pseudo-supervised Deep Subspace Clustering

arXiv: https://arxiv.org/abs/2104.03531 · HTML: https://mlsanity.com/paper/2104.03531/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 76 references that are in the map.
- First posted on arXiv 8 Apr 2021.

## Builds on (most cited first, 30 of 34)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Deep Clustering for Unsupervised Learning of Visual Features](https://mlsanity.com/paper/1807.05520/) (2018)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Self-supervised Visual Feature Learning with Deep Neural Networks: A Survey](https://mlsanity.com/paper/1902.06162/) (2019)
- [Revisiting Self-Supervised Visual Representation Learning](https://mlsanity.com/paper/1901.09005/) (2019)
- [Towards K-means-friendly Spaces: Simultaneous Deep Learning and Clustering](https://mlsanity.com/paper/1610.04794/) (2016)
- [Variational Deep Embedding: An Unsupervised and Generative Approach to Clustering](https://mlsanity.com/paper/1611.05148/) (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 Subspace Clustering Networks](https://mlsanity.com/paper/1709.02508/) (2017)
- [Deep Comprehensive Correlation Mining for Image Clustering](https://mlsanity.com/paper/1904.06925/) (2019)
- [Deep Spectral Clustering using Dual Autoencoder Network](https://mlsanity.com/paper/1904.13113/) (2019)
- [Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit](https://mlsanity.com/paper/1507.01238/) (2015)
- [Deep k-Means: Jointly clustering with k-Means and learning representations](https://mlsanity.com/paper/1806.10069/) (2018)
- [Smooth Neighbors on Teacher Graphs for Semi-supervised Learning](https://mlsanity.com/paper/1711.00258/) (2017)
- [Robust and Efficient Subspace Segmentation via Least Squares Regression](https://mlsanity.com/paper/1404.6736/) (2014)
- [Deep clustering: On the link between discriminative models and K-means](https://mlsanity.com/paper/1810.04246/) (2018)
- [Robust Graph Learning from Noisy Data](https://mlsanity.com/paper/1812.06673/) (2018)
- [Self-Supervised Convolutional Subspace Clustering Network](https://mlsanity.com/paper/1905.00149/) (2019)
- [Deep Multimodal Subspace Clustering Networks](https://mlsanity.com/paper/1804.06498/) (2018)
- [Structured Graph Learning for Scalable Subspace Clustering: From Single-view to Multi-view](https://mlsanity.com/paper/2102.07943/) (2021)
- [Multi-view Deep Subspace Clustering Networks](https://mlsanity.com/paper/1908.01978/) (2019)
- [Structured Graph Learning for Clustering and Semi-supervised Classification](https://mlsanity.com/paper/2008.13429/) (2020)
- [Scalable Deep k-Subspace Clustering](https://mlsanity.com/paper/1811.01045/) (2018)
- [Deep Clustering with a Dynamic Autoencoder: From Reconstruction towards Centroids Construction](https://mlsanity.com/paper/1901.07752/) (2019)
- [Adversarial Deep Embedded Clustering: on a better trade-off between Feature Randomness and Feature Drift](https://mlsanity.com/paper/1909.11832/) (2019)
- [Kernel Sparse Subspace Clustering on Symmetric Positive Definite Manifolds](https://mlsanity.com/paper/1601.00414/) (2016)
- [Structure Learning with Similarity Preserving](https://mlsanity.com/paper/1912.01197/) (2019)

## Built on by (most cited first, 29 of 29)

- [Multi-view Contrastive Graph Clustering](https://mlsanity.com/paper/2110.11842/) (2021)
- [A Comprehensive Survey on Deep Clustering: Taxonomy, Challenges, and Future Directions](https://mlsanity.com/paper/2206.07579/) (2022)
- [Interpretable Deep Clustering for Tabular Data](https://mlsanity.com/paper/2306.04785/) (2023)
- [Self-supervised Contrastive Attributed Graph Clustering](https://mlsanity.com/paper/2110.08264/) (2021)
- [Self-supervised Consensus Representation Learning for Attributed Graph](https://mlsanity.com/paper/2108.04822/) (2021)
- [Self-Supervised Information Bottleneck for Deep Multi-View Subspace Clustering](https://mlsanity.com/paper/2204.12496/) (2022)
- [CDC: A Simple Framework for Complex Data Clustering](https://mlsanity.com/paper/2403.03670/) (2024)
- [A Simple Approach to Automated Spectral Clustering](https://mlsanity.com/paper/2107.12183/) (2021)
- [Adaptive Attribute and Structure Subspace Clustering Network](https://mlsanity.com/paper/2109.13742/) (2021)
- [AnomalyNCD: Towards Novel Anomaly Class Discovery in Industrial Scenarios](https://mlsanity.com/paper/2410.14379/) (2024)
- [High-order Multi-view Clustering for Generic Data](https://mlsanity.com/paper/2209.10838/) (2022)
- [Exploring a Principled Framework for Deep Subspace Clustering](https://mlsanity.com/paper/2503.17288/) (2025)
- [Large-Scale Hyperspectral Image Clustering Using Contrastive Learning](https://mlsanity.com/paper/2111.07945/) (2021)
- [Scalable Multi-view Clustering with Graph Filtering](https://mlsanity.com/paper/2205.09228/) (2022)
- [Adaptive Graph Convolutional Subspace Clustering](https://mlsanity.com/paper/2305.03414/) (2023)
- [Smoothed Multi-View Subspace Clustering](https://mlsanity.com/paper/2106.09875/) (2021)
- [Unsupervised Deep Discriminant Analysis Based Clustering](https://mlsanity.com/paper/2206.04686/) (2022)
- [Deep Double Self-Expressive Subspace Clustering](https://mlsanity.com/paper/2306.11592/) (2023)
- [Automatic Discovery of Disease Subgroups by Contrasting with Healthy Controls](https://mlsanity.com/paper/2605.21301/) (2026)
- [Self-Supervised Deep Subspace Clustering with Entropy-norm](https://mlsanity.com/paper/2206.04958/) (2022)
- [Learning Structure Aware Deep Spectral Embedding](https://mlsanity.com/paper/2305.08215/) (2023)
- [Subspace Clustering in Wavelet Packets Domain](https://mlsanity.com/paper/2406.03819/) (2024)
- [CDFL: Efficient Federated Human Activity Recognition using Contrastive Learning and Deep Clustering](https://mlsanity.com/paper/2407.12287/) (2024)
- [Label-independent hyperparameter-free self-supervised single-view deep subspace clustering](https://mlsanity.com/paper/2504.18179/) (2025)
- [Scalable Context-Preserving Model-Aware Deep Clustering for Hyperspectral Images](https://mlsanity.com/paper/2506.11377/) (2025)
- [One-step Multi-view Clustering With Adaptive Low-rank Anchor-graph Learning](https://mlsanity.com/paper/2509.14724/) (2025)
- [Scalable Deep Subspace Clustering Network](https://mlsanity.com/paper/2512.21434/) (2025)
- [Jointly Learning Structured Representations and Stabilized Affinity for Human Motion Segmentation](https://mlsanity.com/paper/2605.05753/) (2026)
- [Cohort Organized Learning: Clustering Through Agreement](https://mlsanity.com/paper/2606.21743/) (2026)

## Abstract (arXiv)

Auto-Encoder (AE)-based deep subspace clustering (DSC) methods have achieved impressive performance due to the powerful representation extracted using deep neural networks while prioritizing categorical separability. However, self-reconstruction loss of an AE ignores rich useful relation information and might lead to indiscriminative representation, which inevitably degrades the clustering performance. It is also challenging to learn high-level similarity without feeding semantic labels. Another unsolved problem facing DSC is the huge memory cost due to n× n similarity matrix, which is incurred by the self-expression layer between an encoder and decoder. To tackle these problems, we use pairwise similarity to weigh the reconstruction loss to capture local structure information, while a similarity is learned by the self-expression layer. Pseudo-graphs and pseudo-labels, which allow benefiting from uncertain knowledge acquired during network training, are further employed to supervise similarity learning. Joint learning and iterative training facilitate to obtain an overall optimal solution. Extensive experiments on benchmark datasets demonstrate the superiority of our approach. By combining with the k-nearest neighbors algorithm, we further show that our method can address the large-scale and out-of-sample problems.