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arXiv · 1404.0751

Subspace Learning from Extremely Compressed Measurements

Akshay Krishnamurthy·Martin Azizyan·Aarti Singh
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Abstract

We consider learning the principal subspace of a large set of vectors from an extremely small number of compressive measurements of each vector. Our theoretical results show that even a constant number of measurements per column suffices to approximate the principal subspace to arbitrary precision, provided that the number of vectors is large. This result is achieved by a simple algorithm that computes the eigenvectors of an estimate of the covariance matrix. The main insight is to exploit an averaging effect that arises from applying a different random projection to each vector. We provide a number of simulations confirming our theoretical results.

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Akshay Krishnamurthy, Martin Azizyan, Aarti Singh. 2014-04-03. Subspace Learning from Extremely Compressed Measurements. https://arxiv.org/abs/1404.0751

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