Spectral Methods in Machine Learning Reading List

Curated by Mouhssine Rifaki | Stanford Electrical Engineering | Last updated August 2026

Eigenvalue decompositions and spectral techniques for learning, clustering, and dimensionality reduction.

Spectral Methods in Machine Learning: 10 key papers

1. Randomized Numerical Linear Algebra: Foundations & Algorithms
   Martinsson and Tropp. arXiv 2020.
2. Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
   Halko et al. arXiv 2009.
3. A Tutorial on Spectral Clustering
   von Luxburg. arXiv 2007.
4. Spectral Methods for Data Science: A Statistical Perspective
   Chen et al. arXiv 2020.
5. Tensor decompositions for learning latent variable models
   Anandkumar et al. arXiv 2012.
6. A Spectral Algorithm for Learning Hidden Markov Models
   Hsu et al. arXiv 2008.
7. Learning Linear Dynamical Systems via Spectral Filtering
   Hazan et al. arXiv 2017.
8. Spectral Normalization for Generative Adversarial Networks
   Miyato et al. arXiv 2018.
9. Entrywise Eigenvector Analysis of Random Matrices with Low Expected Rank
   Abbe et al. arXiv 2017.
10. Spectral Clustering Based on Local PCA
    Arias-Castro et al. arXiv 2013.

Related reading lists

• Low-Rank Structure in Machine Learning
• System Identification & Learning Dynamical Systems
• Linear MDPs & Linear Function Approximation
• Hyperparameter Optimization & AutoML
• Concentration Inequalities & Empirical Processes
• Game Theory for Multi-Agent Systems
• Score-Based Generative Modeling
• Privacy & Differential Privacy in Machine Learning