@inbook{568089c6c7034b5080a702bf5a9a75cc,
title = "Compressive classification and the rare eclipse problem",
abstract = "This paper addresses the fundamental question of when convex sets remain disjoint after random projection. We provide an analysis using ideas from high-dimensional convex geometry. For ellipsoids, we provide a bound in terms of the distance between these ellipsoids and simple functions of their polynomial coefficients. As an application, this theorem provides bounds for compressive classification of convex sets. Rather than assuming that the data to be classified is sparse, our results show that the data can be acquired via very few measurements yet will remain linearly separable. We demonstrate the feasibility of this approach in the context of hyperspectral imaging.",
keywords = "Compressive classification, Gordon{\textquoteright}s theorem",
author = "Bandeira, {Afonso S.} and Mixon, {Dustin G.} and Benjamin Recht",
note = "Funding Information: Acknowledgements The authors thank Matthew Fickus and Katya Scheinberg for insightful discussions. A. S. Bandeira was supported by AFOSR award FA9550-12-1-0317; D. G. Mixon was supported by NSF award DMS-1321779, AFOSR F4FGA06060J007, and AFOSR Young Investigator Research Program award F4FGA06088J001; and B. Recht was supported by ONR award N00014-11-1-0723 and NSF awards CCF-1139953 and CCF-11482. The views expressed in this article are those of the authors and do not reflect the official policy or position of the US Air Force, Department of Defense, or the US Government. Publisher Copyright: {\textcopyright} Springer International Publishing AG 2017. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.",
year = "2017",
doi = "10.1007/978-3-319-69802-1_6",
language = "English (US)",
series = "Applied and Numerical Harmonic Analysis",
publisher = "Springer International Publishing",
number = "9783319698014",
pages = "197--220",
booktitle = "Applied and Numerical Harmonic Analysis",
edition = "9783319698014",
}