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

## TL;DR

This paper develops a theoretical framework for spectral methods in clustering data near unions of subspaces using random geometry graphs, demonstrating broad conditions for effectiveness and supporting findings with numerical experiments.

## Contribution

It provides the first comprehensive theory analyzing spectral subspace clustering via random geometry graphs, expanding understanding of its efficiency and potential applications.

## Key findings

- Spectral method effectively clusters data near unions of subspaces.
- Theoretical analysis confirms broad conditions for success.
- Numerical experiments validate the theoretical predictions.

## Abstract

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.