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Advances in Probability and Mathematical StatisticsMore About Asymptotic Properties of Some Binary Classification Methods for High Dimensional Data

Advances in Probability and Mathematical Statistics: More About Asymptotic Properties of Some... [In this manuscript we study the asymptotic behavior of the following binary classification methods: Support Vector Machine, Mean Difference, Distance Weighted Discrimination and Maximal Data Piling, when the dimension of the data increases and the sample sizes of the classes are fixed. We consider multivariate data with the asymptotic geometric structure of n-simplex, such that the multivariate standard Gaussian distribution, as the dimension increases and the sample size n is fixed. We provide the asymptotic behavior of the four methods in terms of the angle between the normal vector of the separating hyperplane of the method and the optimal direction for classification, under more general conditions than those of Bolivar-Cime and Cordova-Rodriguez (Commun Stat Theory Methods 47(11):2720–2740, 2018). We also analyze the asymptotic behavior of the probabilities of misclassification of the methods. A simulation study is performed to illustrate the theoretical results.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Advances in Probability and Mathematical StatisticsMore About Asymptotic Properties of Some Binary Classification Methods for High Dimensional Data

Part of the Progress in Probability Book Series (volume 79)
Editors: Hernández‐Hernández, Daniel; Leonardi, Florencia; Mena, Ramsés H.; Pardo Millán, Juan Carlos
Bolivar-Cime, Addy
Advances in Probability and Mathematical Statistics — Aug 5, 2021
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References (20)

Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
ISBN
978-3-030-85324-2
Pages
43 –57
DOI
10.1007/978-3-030-85325-9_3
Publisher site
See Chapter on Publisher Site

Abstract

[In this manuscript we study the asymptotic behavior of the following binary classification methods: Support Vector Machine, Mean Difference, Distance Weighted Discrimination and Maximal Data Piling, when the dimension of the data increases and the sample sizes of the classes are fixed. We consider multivariate data with the asymptotic geometric structure of n-simplex, such that the multivariate standard Gaussian distribution, as the dimension increases and the sample size n is fixed. We provide the asymptotic behavior of the four methods in terms of the angle between the normal vector of the separating hyperplane of the method and the optimal direction for classification, under more general conditions than those of Bolivar-Cime and Cordova-Rodriguez (Commun Stat Theory Methods 47(11):2720–2740, 2018). We also analyze the asymptotic behavior of the probabilities of misclassification of the methods. A simulation study is performed to illustrate the theoretical results.]

Published: Aug 5, 2021

Keywords: High dimensional data; Binary discrimination; Asymptotic behavior; Machine learning; Support vector machine

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