# Theory of Spectral Method for Union of Subspaces-Based Random Geometry Graph

arXiv: https://arxiv.org/abs/1907.10906 · HTML: https://mlsanity.com/paper/1907.10906/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jul 2019.

## Built on by (most cited first, 2 of 2)

- [Breaking the Curse of Dimensionality: Diffusion Models Efficiently Learn Low-Dimensional Distributions](https://mlsanity.com/paper/2409.02426/) (2024)
- [Convergence and Recovery Guarantees of the K-Subspaces Method for Subspace Clustering](https://mlsanity.com/paper/2206.05553/) (2022)

## Abstract (arXiv)

Spectral Method is a commonly used scheme to cluster data points lying close to Union of Subspaces by first constructing a Random Geometry Graph, called Subspace Clustering. This paper establishes a theory to analyze this method. Based on this theory, we demonstrate the efficiency of Subspace Clustering in fairly broad conditions. The insights and analysis techniques developed in this paper might also have implications for other random graph problems. Numerical experiments demonstrate the effectiveness of our theoretical study.