Corpus ID: 207780368

# Optimality of Spectral Clustering for Gaussian Mixture Model

@article{Lffler2019OptimalityOS,
title={Optimality of Spectral Clustering for Gaussian Mixture Model},
author={Matthias L{\"o}ffler and A. Zhang and H. Zhou},
journal={ArXiv},
year={2019},
volume={abs/1911.00538}
}
• Published 2019
• Mathematics, Computer Science
• ArXiv
Spectral clustering is one of the most popular algorithms to group high dimensional data. It is easy to implement and computationally efficient. Despite its popularity and successful applications, its theoretical properties have not been fully understood. In this paper, we show that spectral clustering is minimax optimal in the Gaussian Mixture Model with isotropic covariance matrix, when the number of clusters is fixed and the signal-to-noise ratio is large enough. Spectral gap conditions are… Expand
14 Citations

#### References

SHOWING 1-10 OF 95 REFERENCES
Statistical analysis of finite mixture distributions
• Mathematics
• 1986
• 3,354
• Highly Influential
FAST COMMUNITY DETECTION BY SCORE
• J. Jin
• Mathematics, Computer Science
• 2015
• 175
• Highly Influential
• PDF
An 𝓁p theory of PCA and spectral clustering
• Mathematics, Computer Science
• ArXiv
• 2020
• 4
Cutoff for exact recovery of Gaussian mixture models
• Mathematics, Computer Science
• ArXiv
• 2020
• 4
• PDF
Cuto↵ for exact recovery of gaussian mixture models
• arXiv preprint,
• 2020
ENTRYWISE EIGENVECTOR ANALYSIS OF RANDOM MATRICES WITH LOW EXPECTED RANK.
• Medicine, Mathematics
• Annals of statistics
• 2020
• 114
• PDF