# Revisiting data augmentation for subspace clustering

arXiv: https://arxiv.org/abs/2207.09728 · HTML: https://mlsanity.com/paper/2207.09728/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 66 references that are in the map.
- First posted on arXiv 20 Jul 2022.

## Builds on (most cited first, 21 of 21)

- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Unsupervised Data Augmentation for Consistency Training](https://mlsanity.com/paper/1904.12848/) (2019)
- [The Effectiveness of Data Augmentation in Image Classification using Deep Learning](https://mlsanity.com/paper/1712.04621/) (2017)
- [Fast AutoAugment](https://mlsanity.com/paper/1905.00397/) (2019)
- [MixUp as Locally Linear Out-Of-Manifold Regularization](https://mlsanity.com/paper/1809.02499/) (2018)
- [A Survey on Data Augmentation for Text Classification](https://mlsanity.com/paper/2107.03158/) (2021)
- [Data Augmentation by Pairing Samples for Images Classification](https://mlsanity.com/paper/1801.02929/) (2018)
- [Deep Subspace Clustering Networks](https://mlsanity.com/paper/1709.02508/) (2017)
- [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)
- [Noisy Sparse Subspace Clustering](https://mlsanity.com/paper/1309.1233/) (2013)
- [Stochastic Sparse Subspace Clustering](https://mlsanity.com/paper/2005.01449/) (2020)
- [Robust Subspace Clustering via Thresholding](https://mlsanity.com/paper/1307.4891/) (2013)
- [On Geometric Analysis of Affine Sparse Subspace Clustering](https://mlsanity.com/paper/1808.05965/) (2018)
- [Is an Affine Constraint Needed for Affine Subspace Clustering?](https://mlsanity.com/paper/2005.03888/) (2020)
- [Correlation Adaptive Subspace Segmentation by Trace Lasso](https://mlsanity.com/paper/1501.04276/) (2015)
- [Innovation Pursuit: A New Approach to Subspace Clustering](https://mlsanity.com/paper/1512.00907/) (2015)
- [Scalable and Robust Sparse Subspace Clustering Using Randomized Clustering and Multilayer Graphs](https://mlsanity.com/paper/1802.07648/) (2018)
- [Correntropy Induced L2 Graph for Robust Subspace Clustering](https://mlsanity.com/paper/1501.04277/) (2015)

## Abstract (arXiv)

Subspace clustering is the classical problem of clustering a collection of data samples that approximately lie around several low-dimensional subspaces. The current state-of-the-art approaches for this problem are based on the self-expressive model which represents the samples as linear combination of other samples. However, these approaches require sufficiently well-spread samples for accurate representation which might not be necessarily accessible in many applications. In this paper, we shed light on this commonly neglected issue and argue that data distribution within each subspace plays a critical role in the success of self-expressive models. Our proposed solution to tackle this issue is motivated by the central role of data augmentation in the generalization power of deep neural networks. We propose two subspace clustering frameworks for both unsupervised and semi-supervised settings that use augmented samples as an enlarged dictionary to improve the quality of the self-expressive representation. We present an automatic augmentation strategy using a few labeled samples for the semi-supervised problem relying on the fact that the data samples lie in the union of multiple linear subspaces. Experimental results confirm the effectiveness of data augmentation, as it significantly improves the performance of general self-expressive models.