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arXiv · 1902.00104

Phase Transition in the Recovery of Rank One Matrices Corrupted by Gaussian Noise

Enrico Au-Yeung·Greg Zanotti
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Abstract

In datasets where the number of parameters is fixed and the number of samples is large, principal component analysis (PCA) is a powerful dimension reduction tool. However, in many contemporary datasets, when the number of parameters is comparable to the sample size, PCA can be misleading. A closely related problem is the following: is it possible to recover a rank-one matrix in the presence of a large amount of noise? In both situations, there is a phase transition in the eigen-structure of the matrix.

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Enrico Au-Yeung, Greg Zanotti. 2019-02-13. Phase Transition in the Recovery of Rank One Matrices Corrupted by Gaussian Noise. https://arxiv.org/abs/1902.00104

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