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dc.contributor.authorNiyazi, Lama B.
dc.contributor.authorKammoun, Abla
dc.contributor.authorDahrouj, Hayssam
dc.contributor.authorAlouini, Mohamed-Slim
dc.contributor.authorAl-Naffouri, Tareq Y.
dc.identifier.citationNiyazi, L. B., Kammoun, A., Dahrouj, H., Alouini, M.-S., & Al-Naffouri, T. Y. (2020). Asymptotic Analysis of an Ensemble of Randomly Projected Linear Discriminants. IEEE Journal on Selected Areas in Information Theory, 1–1. doi:10.1109/jsait.2020.3042137
dc.description.abstractDatasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order to rectify the issues associated with classification in such a setting, the classifier in durrant2013random, composed of an ensemble of randomly projected linear discriminants, seems especially promising; it is computationally efficient and, with the optimal projection dimension parameter setting, is competitive with the state-of-the-art. In this work, we seek to further understand the behavior of this classifier through asymptotic analysis. Under the assumption of a growth regime in which the dataset and projection dimensions grow at constant rates to each other, we use random matrix theory to derive asymptotic misclassification probabilities showing the effect of the ensemble as a regularization of the data sample covariance matrix. The asymptotic errors further help to identify situations in which the ensemble offers a performance advantage. We also develop a consistent estimator of the misclassification probability as an alternative to the computationally-costly cross-validation estimator, which is conventionally used for parameter tuning. Finally, we demonstrate the use of our estimator for tuning the projection dimension on both real and synthetic data.
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)
dc.rights(c) 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
dc.subjectrandom projection
dc.subjectsmall sample issue
dc.subjectrandom matrix theory
dc.subjectgeneralized consistent estimator.
dc.titleAsymptotic Analysis of an Ensemble of Randomly Projected Linear Discriminants
dc.contributor.departmentElectrical Engineering Program, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia.
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentElectrical Engineering Program
dc.identifier.journalIEEE Journal on Selected Areas in Information Theory
dc.contributor.institutionDepartment of Electrical and Computer Engineering, Effat University, Jeddah, Saudi Arabia.
kaust.personNiyazi, Lama B.
kaust.personKammoun, Abla
kaust.personDahrouj, Hayssam
kaust.personAlouini, Mohamed-Slim
kaust.personAl-Naffouri, Tareq Y.

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