# Robust and Efficient Subspace Segmentation via Least Squares Regression

arXiv: https://arxiv.org/abs/1404.6736 · HTML: https://mlsanity.com/paper/1404.6736/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Apr 2014.

## Built on by (most cited first, 30 of 47)

- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Deep Clustering: A Comprehensive Survey](https://mlsanity.com/paper/2210.04142/) (2022)
- [Structured Graph Learning for Scalable Subspace Clustering: From Single-view to Multi-view](https://mlsanity.com/paper/2102.07943/) (2021)
- [Pseudo-supervised Deep Subspace Clustering](https://mlsanity.com/paper/2104.03531/) (2021)
- [Learning a Self-Expressive Network for Subspace Clustering](https://mlsanity.com/paper/2110.04318/) (2021)
- [Graph Condensation: A Survey](https://mlsanity.com/paper/2401.11720/) (2024)
- [Image Clustering via the Principle of Rate Reduction in the Age of Pretrained Models](https://mlsanity.com/paper/2306.05272/) (2023)
- [Unpaired Multi-View Graph Clustering with Cross-View Structure Matching](https://mlsanity.com/paper/2307.03476/) (2023)
- [Learning segmentation from point trajectories](https://mlsanity.com/paper/2501.12392/) (2025)
- [Towards Clustering-friendly Representations: Subspace Clustering via Graph Filtering](https://mlsanity.com/paper/2106.09874/) (2021)
- [A Novel Approach for Effective Multi-View Clustering with Information-Theoretic Perspective](https://mlsanity.com/paper/2309.13989/) (2023)
- [Unsupervised Manifold Linearizing and Clustering](https://mlsanity.com/paper/2301.01805/) (2023)
- [A Simple Approach to Automated Spectral Clustering](https://mlsanity.com/paper/2107.12183/) (2021)
- [A Comprehensive Survey on Spectral Clustering with Graph Structure Learning](https://mlsanity.com/paper/2501.13597/) (2025)
- [Adaptive Attribute and Structure Subspace Clustering Network](https://mlsanity.com/paper/2109.13742/) (2021)
- [Consistency and Diversity induced Human Motion Segmentation](https://mlsanity.com/paper/2202.04861/) (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)
- [Spectral Subspace Clustering for Attributed Graphs](https://mlsanity.com/paper/2411.11074/) (2024)
- [Nonlinear subspace clustering by functional link neural networks](https://mlsanity.com/paper/2402.02051/) (2024)
- [Graph Constrained Data Representation Learning for Human Motion Segmentation](https://mlsanity.com/paper/2107.13362/) (2021)
- [Adaptive Graph Convolutional Subspace Clustering](https://mlsanity.com/paper/2305.03414/) (2023)
- [Deep Double Self-Expressive Subspace Clustering](https://mlsanity.com/paper/2306.11592/) (2023)
- [Learning a Gaussian Mixture for Sparsity Regularization in Inverse Problems](https://mlsanity.com/paper/2401.16612/) (2024)
- [Learning idempotent representation for subspace clustering](https://mlsanity.com/paper/2207.14431/) (2022)
- [PMSSC: Parallelizable multi-subset based self-expressive model for subspace clustering](https://mlsanity.com/paper/2111.12232/) (2021)
- [Attentive Multi-View Deep Subspace Clustering Net](https://mlsanity.com/paper/2112.12506/) (2021)
- [C2IMUFS: Complementary and Consensus Learning-based Incomplete Multi-view Unsupervised Feature Selection](https://mlsanity.com/paper/2208.09736/) (2022)
- [Hyper-Laplacian Regularized Concept Factorization in Low-rank Tensor Space for Multi-view Clustering](https://mlsanity.com/paper/2304.11435/) (2023)
- [Graph Cuts with Arbitrary Size Constraints Through Optimal Transport](https://mlsanity.com/paper/2402.04732/) (2024)

## Abstract (arXiv)

This paper studies the subspace segmentation problem which aims to segment data drawn from a union of multiple linear subspaces. Recent works by using sparse representation, low rank representation and their extensions attract much attention. If the subspaces from which the data drawn are independent or orthogonal, they are able to obtain a block diagonal affinity matrix, which usually leads to a correct segmentation. The main differences among them are their objective functions. We theoretically show that if the objective function satisfies some conditions, and the data are sufficiently drawn from independent subspaces, the obtained affinity matrix is always block diagonal. Furthermore, the data sampling can be insufficient if the subspaces are orthogonal. Some existing methods are all special cases. Then we present the Least Squares Regression (LSR) method for subspace segmentation. It takes advantage of data correlation, which is common in real data. LSR encourages a grouping effect which tends to group highly correlated data together. Experimental results on the Hopkins 155 database and Extended Yale Database B show that our method significantly outperforms state-of-the-art methods. Beyond segmentation accuracy, all experiments demonstrate that LSR is much more efficient.