# Subspace Clustering via Thresholding and Spectral Clustering

arXiv: https://arxiv.org/abs/1303.3716 · HTML: https://mlsanity.com/paper/1303.3716/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2013.

## Built on by (most cited first, 4 of 4)

- [Mitigating exponential concentration in covariant quantum kernels for subspace and real-world data](https://mlsanity.com/paper/2412.07915/) (2024)
- [PointCLM: A Contrastive Learning-based Framework for Multi-instance Point Cloud Registration](https://mlsanity.com/paper/2209.00219/) (2022)
- [PMSSC: Parallelizable multi-subset based self-expressive model for subspace clustering](https://mlsanity.com/paper/2111.12232/) (2021)
- [Enriched Robust Multi-View Kernel Subspace Clustering](https://mlsanity.com/paper/2205.10495/) (2022)

## Abstract (arXiv)

We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity clustering algorithm based on thresholding the correlations between the data points followed by spectral clustering. A probabilistic performance analysis shows that this algorithm succeeds even when the subspaces intersect, and when the dimensions of the subspaces scale (up to a log-factor) linearly in the ambient dimension. Moreover, we prove that the algorithm also succeeds for data points that are subject to erasures with the number of erasures scaling (up to a log-factor) linearly in the ambient dimension. Finally, we propose a simple scheme that provably detects outliers.