Compressive classification and the rare eclipse problem

Afonso Bandeira, Dustin G. Mixon, Benjamin Recht

Research output: Chapter in Book/Report/Conference proceedingChapter

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.

Original languageEnglish (US)
Title of host publicationApplied and Numerical Harmonic Analysis
PublisherSpringer International Publishing
Pages197-220
Number of pages24
Edition9783319698014
DOIs
StatePublished - Jan 1 2017

Publication series

NameApplied and Numerical Harmonic Analysis
Number9783319698014
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017

Fingerprint

Ellipsoid
Convex Sets
Polynomials
Random Projection
Convex Geometry
Hyperspectral Imaging
Geometry
Disjoint
High-dimensional
Linearly
Polynomial
Coefficient
Theorem
Demonstrate
Hyperspectral imaging
Context

Keywords

  • Compressive classification
  • Gordon’s theorem

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Bandeira, A., Mixon, D. G., & Recht, B. (2017). Compressive classification and the rare eclipse problem. In Applied and Numerical Harmonic Analysis (9783319698014 ed., pp. 197-220). (Applied and Numerical Harmonic Analysis; No. 9783319698014). Springer International Publishing. https://doi.org/10.1007/978-3-319-69802-1_6

Compressive classification and the rare eclipse problem. / Bandeira, Afonso; Mixon, Dustin G.; Recht, Benjamin.

Applied and Numerical Harmonic Analysis. 9783319698014. ed. Springer International Publishing, 2017. p. 197-220 (Applied and Numerical Harmonic Analysis; No. 9783319698014).

Research output: Chapter in Book/Report/Conference proceedingChapter

Bandeira, A, Mixon, DG & Recht, B 2017, Compressive classification and the rare eclipse problem. in Applied and Numerical Harmonic Analysis. 9783319698014 edn, Applied and Numerical Harmonic Analysis, no. 9783319698014, Springer International Publishing, pp. 197-220. https://doi.org/10.1007/978-3-319-69802-1_6
Bandeira A, Mixon DG, Recht B. Compressive classification and the rare eclipse problem. In Applied and Numerical Harmonic Analysis. 9783319698014 ed. Springer International Publishing. 2017. p. 197-220. (Applied and Numerical Harmonic Analysis; 9783319698014). https://doi.org/10.1007/978-3-319-69802-1_6
Bandeira, Afonso ; Mixon, Dustin G. ; Recht, Benjamin. / Compressive classification and the rare eclipse problem. Applied and Numerical Harmonic Analysis. 9783319698014. ed. Springer International Publishing, 2017. pp. 197-220 (Applied and Numerical Harmonic Analysis; 9783319698014).
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