Bounds on the Number of Measurements for Reliable Compressive Classification

Published

Conference Paper

© 1991-2012 IEEE. This paper studies the classification of high-dimensional Gaussian signals from low-dimensional noisy, linear measurements. In particular, it provides upper bounds (sufficient conditions) on the number of measurements required to drive the probability of misclassification to zero in the low-noise regime, both for random measurements and designed ones. Such bounds reveal two important operational regimes that are a function of the characteristics of the source: 1) when the number of classes is less than or equal to the dimension of the space spanned by signals in each class, reliable classification is possible in the low-noise regime by using a one-vs-all measurement design; 2) when the dimension of the spaces spanned by signals in each class is lower than the number of classes, reliable classification is guaranteed in the low-noise regime by using a simple random measurement design. Simulation results both with synthetic and real data show that our analysis is sharp, in the sense that it is able to gauge the number of measurements required to drive the misclassification probability to zero in the low-noise regime.

Full Text

Duke Authors

Cited Authors

  • Reboredo, H; Renna, F; Calderbank, R; Rodrigues, MRD

Published Date

  • November 15, 2016

Published In

Volume / Issue

  • 64 / 22

Start / End Page

  • 5778 - 5793

International Standard Serial Number (ISSN)

  • 1053-587X

Digital Object Identifier (DOI)

  • 10.1109/TSP.2016.2599496

Citation Source

  • Scopus