Random Laplacian Matrices and Convex Relaxations

@article{Bandeira2018RandomLM,
  title={Random Laplacian Matrices and Convex Relaxations},
  author={A. Bandeira},
  journal={Foundations of Computational Mathematics},
  year={2018},
  volume={18},
  pages={345-379}
}
  • A. Bandeira
  • Published 2018
  • Mathematics, Computer Science
  • Foundations of Computational Mathematics
  • The largest eigenvalue of a matrix is always larger or equal than its largest diagonal entry. We show that for a class of random Laplacian matrices with independent off-diagonal entries, this bound is essentially tight: the largest eigenvalue is, up to lower order terms, often the size of the largest diagonal. entry. Besides being a simple tool to obtain precise estimates on the largest eigenvalue of a class of random Laplacian matrices, our main result settles a number of open problems related… CONTINUE READING
    66 Citations
    Unified $\ell_{2\rightarrow\infty}$ Eigenspace Perturbation Theory for Symmetric Random Matrices
    • 6
    • Highly Influenced
    • PDF
    Entrywise Eigenvector Analysis of Random Matrices with Low Expected Rank
    • 96
    • Highly Influenced
    • PDF
    Strong Consistency, Graph Laplacians, and the Stochastic Block Model
    • 2
    • PDF
    Certifying Global Optimality of Graph Cuts via Semidefinite Relaxation: A Performance Guarantee for Spectral Clustering
    • 10
    • Highly Influenced
    • PDF
    Achieving Exact Cluster Recovery Threshold via Semidefinite Programming
    • 164
    • PDF
    Achieving Exact Cluster Recovery Threshold via Semidefinite Programming
    • 11
    Optimal Bipartite Network Clustering
    • 11
    • PDF
    Spectral Clustering Revisited: Information Hidden in the Fiedler Vector
    Tightness of the maximum likelihood semidefinite relaxation for angular synchronization
    • 87
    • PDF

    References

    SHOWING 1-10 OF 59 REFERENCES
    SPECTRAL DISTRIBUTIONS OF ADJACENCY AND LAPLACIAN MATRICES OF RANDOM GRAPHS
    • 77
    • PDF
    Spectral measure of large random Hankel, Markov and Toeplitz matrices
    • 194
    • PDF
    Spectral graph theory
    • 1,978
    • PDF
    User-Friendly Tail Bounds for Sums of Random Matrices
    • J. Tropp
    • Mathematics, Computer Science
    • Found. Comput. Math.
    • 2012
    • 1,191
    • PDF
    Achieving Exact Cluster Recovery Threshold via Semidefinite Programming
    • 164
    • PDF
    A Proof of the Block Model Threshold Conjecture
    • 217
    • PDF
    A Cheeger Inequality for the Graph Connection Laplacian
    • 105
    • PDF
    Angular Synchronization by Eigenvectors and Semidefinite Programming.
    • A. Singer
    • Mathematics, Medicine
    • Applied and computational harmonic analysis
    • 2011
    • 263
    • PDF
    Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
    • F. Alizadeh
    • Mathematics, Computer Science
    • SIAM J. Optim.
    • 1995
    • 931
    • PDF