Under sparse heterogeneous random noise, eigenspace perturbation bounds are derived via QVE and isotropic local laws that explicitly separate a structured geometric bias term from signal-to-noise and fluctuation contributions.
Unified \ ell\_\ 2 rightarrow infty\ \ Eigenspace Perturbation Theory for Symmetric Random Matrices
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UNVERDICTED 4representative citing papers
Proves approximate Gaussianity of debiased linear forms of eigenvectors in matrix denoising and spiked PCA models under Gaussian noise, then constructs bias/variance estimators yielding minimax-optimal confidence intervals without sample splitting.
Develops a toolbox for two-to-infinity norm bounds on eigenvector deviations under multiple assumption sets and derives generic conditions for perfect clustering
Lloyd's algorithm on perturbed sub-Gaussian mixture samples has exponentially bounded mis-clustering rate after O(log n) iterations when initialized properly and perturbation is small relative to noise.
citing papers explorer
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Geometric bias in eigenspace perturbation under random heterogeneous noise
Under sparse heterogeneous random noise, eigenspace perturbation bounds are derived via QVE and isotropic local laws that explicitly separate a structured geometric bias term from signal-to-noise and fluctuation contributions.
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Statistical Inference for Linear Functions of Eigenvectors with Small Eigengaps
Proves approximate Gaussianity of debiased linear forms of eigenvectors in matrix denoising and spiked PCA models under Gaussian noise, then constructs bias/variance estimators yielding minimax-optimal confidence intervals without sample splitting.
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Davis-Kahan Theorem in the two-to-infinity norm and its application to perfect clustering
Develops a toolbox for two-to-infinity norm bounds on eigenvector deviations under multiple assumption sets and derives generic conditions for perfect clustering
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Consistency of Lloyd's Algorithm Under Perturbations
Lloyd's algorithm on perturbed sub-Gaussian mixture samples has exponentially bounded mis-clustering rate after O(log n) iterations when initialized properly and perturbation is small relative to noise.