Asymptotic Performance of Linear Discriminant Analysis with Random Projections

Khalil Elkhalil, Abla Kammoun, Robert Calderbank, Tareq Y. Al-Naffouri, Mohamed-Slim Alouini

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

We investigate random projections in the context of randomly projected linear discriminant analysis (LDA). We consider the case in which the data of dimension p is randomly projected onto a lower dimensional space before being fed to the classifier. Using fundamental results from random matrix theory and relying on some mild assumptions, we show that the asymptotic performance in terms of probability of misclassification approaches a deterministic quantity that only depends on the data statistics and the dimensions involved. Such results permits to reliably predict the performance of projected LDA as a function of the reduced dimension d < p and thus helps to determine the minimum d to achieve a certain desired performance. Finally, we validate our results with finite-sample settings drawn from both synthetic data and the popular MNIST dataset.
Original languageEnglish (US)
Title of host publicationICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages3472-3476
Number of pages5
ISBN (Print)9781479981311
DOIs
StatePublished - May 2019

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