Subspace Learning from Extremely Compressed Measurements
Machine Learning
2016-12-13 v2 Machine Learning
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.
Cite
@article{arxiv.1404.0751,
title = {Subspace Learning from Extremely Compressed Measurements},
author = {Akshay Krishnamurthy and Martin Azizyan and Aarti Singh},
journal= {arXiv preprint arXiv:1404.0751},
year = {2016}
}