Carnegie Mellon University
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Subspace Learning from Extremely Compressed Measurements

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journal contribution
posted on 2014-04-04, 00:00 authored by Akshay Krishnamurthy, Martin Azizyan, Aarti Singh

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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