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Bounds on the Number of Measurements for Reliable Compressive Classification

Reboredo, H; Renna, F; Calderbank, R; Rodrigues, MRD; (2016) Bounds on the Number of Measurements for Reliable Compressive Classification. IEEE Transactions on Signal Processing , 64 (22) pp. 5778-5793. 10.1109/TSP.2016.2599496. Green open access

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Abstract

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.

Type: Article
Title: Bounds on the Number of Measurements for Reliable Compressive Classification
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/TSP.2016.2599496
Publisher version: http://doi.org/10.1109/TSP.2016.2599496
Language: English
Additional information: This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/
Keywords: Science & Technology, Technology, Engineering, Electrical & Electronic, Engineering, Compressed sensing, compressive classification, classification, dimensionality reduction, Gaussian mixture models, measurement design, phase transitions, random measurements, TASK-SPECIFIC INFORMATION, LINEAR-SUBSPACES, FACE RECOGNITION, FEATURE-EXTRACTION, GAUSSIAN MIXTURE, RECONSTRUCTION, SIGNALS, ALGORITHM, MANIFOLDS, RECOVERY
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Electronic and Electrical Eng
URI: https://discovery.ucl.ac.uk/id/eprint/1529768
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