Compressive Classification: Where Wireless Communications Meets Machine Learning

  • Miguel RodriguesEmail author
  • Matthew Nokleby
  • Francesco Renna
  • Robert Calderbank
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


This chapter introduces Shannon-inspired performance limits associated with the classification of low-dimensional subspaces embedded in a high-dimensional ambient space from compressive and noisy measurements. In particular, it introduces the diversity-discrimination tradeoff that describes the interplay between the number of classes that can be separated by a compressive classifier—measured via the discrimination gain—and the performance of such a classifier—measured via the diversity gain—and the relation of such an interplay to the underlying problem geometry, including the ambient space dimension, the subspaces dimension, and the number of compressive measurements. Such a fundamental limit on performance is derived from a syntactic equivalence between the compressive classification problem and certain wireless communications problems. This equivalence provides an opportunity to cross-pollinate ideas between the wireless information theory domain and the compressive classification domain. This chapter also demonstrates how theory aligns with practice in a concrete application: face recognition from a set of noisy compressive measurements.


Wireless Communication Diversity Gain Grassmann Manifold Noisy Measurement Subspace Dimension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported by the Royal Society International Exchanges Scheme IE120996. The work of Robert Calderbank and Matthew Nokleby is also supported in part by the Air Force Office of Scientific Research under the Complex Networks Program.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Miguel Rodrigues
    • 1
    Email author
  • Matthew Nokleby
    • 2
  • Francesco Renna
    • 3
  • Robert Calderbank
    • 2
  1. 1.Department of Electronic and Electrical EngineeringUniversity College LondonLondonUK
  2. 2.Department of Electrical and Computer EngineeringDuke UniversityDurhamUSA
  3. 3.Department of Computer ScienceInstituto de Telecomunicações, University of PortoPortoPortugal

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