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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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.
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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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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.