Singular Vector Perturbation under Gaussian Noise
arXiv:1208.181135 citationsh-index: 2
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For researchers in statistical learning and signal processing, this offers theoretical tools for uncertainty quantification in PCA and related methods.
The paper provides non-asymptotic conditions under which the first few singular vectors of a matrix perturbed by Gaussian noise are approximately normally distributed, enabling error analysis in linear dimension reduction.
We perform a non-asymptotic analysis on the singular vector distribution under Gaussian noise. In particular, we provide sufficient conditions on a matrix for its first few singular vectors to have near normal distribution. Our result can be used to facilitate the error analysis in linear dimension reduction.