# Beyond Linear Subspace Clustering: A Comparative Study of Nonlinear Manifold Clustering Algorithms

arXiv: https://arxiv.org/abs/2103.10656 · HTML: https://mlsanity.com/paper/2103.10656/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 155 references that are in the map.
- First posted on arXiv 19 Mar 2021.

## Builds on (most cited first, 30 of 32)

- [Confident Learning: Estimating Uncertainty in Dataset Labels](https://mlsanity.com/paper/1911.00068/) (2019)
- [Automated Curriculum Learning for Neural Networks](https://mlsanity.com/paper/1704.03003/) (2017)
- [Joint Unsupervised Learning of Deep Representations and Image Clusters](https://mlsanity.com/paper/1604.03628/) (2016)
- [Deep Subspace Clustering Networks](https://mlsanity.com/paper/1709.02508/) (2017)
- [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)
- [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)
- [Why Are Convolutional Nets More Sample-Efficient than Fully-Connected Nets?](https://mlsanity.com/paper/2010.08515/) (2020)
- [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)
- [Neural Collaborative Subspace Clustering](https://mlsanity.com/paper/1904.10596/) (2019)
- [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)
- [Robust Subspace Clustering via Thresholding](https://mlsanity.com/paper/1307.4891/) (2013)
- [Twin Learning for Similarity and Clustering: A Unified Kernel Approach](https://mlsanity.com/paper/1705.00678/) (2017)
- [Scalable Deep k-Subspace Clustering](https://mlsanity.com/paper/1811.01045/) (2018)
- [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)
- [Correlation Adaptive Subspace Segmentation by Trace Lasso](https://mlsanity.com/paper/1501.04276/) (2015)
- [Scalable and Robust Sparse Subspace Clustering Using Randomized Clustering and Multilayer Graphs](https://mlsanity.com/paper/1802.07648/) (2018)
- [Low-rank Kernel Learning for Graph-based Clustering](https://mlsanity.com/paper/1903.05962/) (2019)
- [Multi-Level Representation Learning for Deep Subspace Clustering](https://mlsanity.com/paper/2001.08533/) (2020)
- [Deep Closed-Form Subspace Clustering](https://mlsanity.com/paper/1908.09419/) (2019)
- [Correntropy Induced L2 Graph for Robust Subspace Clustering](https://mlsanity.com/paper/1501.04277/) (2015)
- [Efficient Solvers for Sparse Subspace Clustering](https://mlsanity.com/paper/1804.06291/) (2018)
- [Laplacian LRR on Product Grassmann Manifolds for Human Activity Clustering in Multi-Camera Video Surveillance](https://mlsanity.com/paper/1606.03838/) (2016)
- [Efficient Sparse Subspace Clustering by Nearest Neighbour Filtering](https://mlsanity.com/paper/1704.03958/) (2017)
- [Self-weighted Multiple Kernel Learning for Graph-based Clustering and Semi-supervised Classification](https://mlsanity.com/paper/1806.07697/) (2018)

## Abstract (arXiv)

Subspace clustering is an important unsupervised clustering approach. It is based on the assumption that the high-dimensional data points are approximately distributed around several low-dimensional linear subspaces. The majority of the prominent subspace clustering algorithms rely on the representation of the data points as linear combinations of other data points, which is known as a self-expressive representation. To overcome the restrictive linearity assumption, numerous nonlinear approaches were proposed to extend successful subspace clustering approaches to data on a union of nonlinear manifolds. In this comparative study, we provide a comprehensive overview of nonlinear subspace clustering approaches proposed in the last decade. We introduce a new taxonomy to classify the state-of-the-art approaches into three categories, namely locality preserving, kernel based, and neural network based. The major representative algorithms within each category are extensively compared on carefully designed synthetic and real-world data sets. The detailed analysis of these approaches unfolds potential research directions and unsolved challenges in this field.