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Discriminant Analysis with Singular Covariance Matrices: Methods and Applications to Spectroscopic Data

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Discriminant Analysis with Singular Covariance Matrices: Methods and Applications to Spectroscopic Data. / Krzanowski, W. J.; Jonathan, P.; McCarthy, W. V. et al.
In: Journal of the Royal Statistical Society: Series C (Applied Statistics), Vol. 44, No. 1, 1995, p. 101-115.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Krzanowski, WJ, Jonathan, P, McCarthy, WV & Thomas, MR 1995, 'Discriminant Analysis with Singular Covariance Matrices: Methods and Applications to Spectroscopic Data', Journal of the Royal Statistical Society: Series C (Applied Statistics), vol. 44, no. 1, pp. 101-115. https://doi.org/10.2307/2986198

APA

Krzanowski, W. J., Jonathan, P., McCarthy, W. V., & Thomas, M. R. (1995). Discriminant Analysis with Singular Covariance Matrices: Methods and Applications to Spectroscopic Data. Journal of the Royal Statistical Society: Series C (Applied Statistics), 44(1), 101-115. https://doi.org/10.2307/2986198

Vancouver

Krzanowski WJ, Jonathan P, McCarthy WV, Thomas MR. Discriminant Analysis with Singular Covariance Matrices: Methods and Applications to Spectroscopic Data. Journal of the Royal Statistical Society: Series C (Applied Statistics). 1995;44(1):101-115. doi: 10.2307/2986198

Author

Krzanowski, W. J. ; Jonathan, P. ; McCarthy, W. V. et al. / Discriminant Analysis with Singular Covariance Matrices : Methods and Applications to Spectroscopic Data. In: Journal of the Royal Statistical Society: Series C (Applied Statistics). 1995 ; Vol. 44, No. 1. pp. 101-115.

Bibtex

@article{470fa4d5196b42ee922f526aa7066829,
title = "Discriminant Analysis with Singular Covariance Matrices: Methods and Applications to Spectroscopic Data",
abstract = "Currently popular techniques such as experimental spectroscopy and computer-aided molecular modelling lead to data having very many variables observed on each of relatively few individuals. A common objective is discrimination between two or more groups, but the direct application of standard discriminant methodology fails because of singularity of covariance matrices. The problem has been circumvented in the past by prior selection of a few transformed variables, using either principal component analysis or partial least squares. Although such selection ensures non-singularity of matrices, the decision process is arbitrary and valuable information on group structure may be lost. We therefore consider some ways of estimating linear discriminant functions without such prior selection. Several spectroscopic data sets are analysed with each method, and questions of bias of assessment procedures are investigated. All proposed methods seem worthy of consideration in practice.",
author = "Krzanowski, {W. J.} and P. Jonathan and McCarthy, {W. V.} and Thomas, {M. R.}",
year = "1995",
doi = "10.2307/2986198",
language = "English",
volume = "44",
pages = "101--115",
journal = "Journal of the Royal Statistical Society: Series C (Applied Statistics)",
issn = "0035-9254",
publisher = "Wiley-Blackwell",
number = "1",

}

RIS

TY - JOUR

T1 - Discriminant Analysis with Singular Covariance Matrices

T2 - Methods and Applications to Spectroscopic Data

AU - Krzanowski, W. J.

AU - Jonathan, P.

AU - McCarthy, W. V.

AU - Thomas, M. R.

PY - 1995

Y1 - 1995

N2 - Currently popular techniques such as experimental spectroscopy and computer-aided molecular modelling lead to data having very many variables observed on each of relatively few individuals. A common objective is discrimination between two or more groups, but the direct application of standard discriminant methodology fails because of singularity of covariance matrices. The problem has been circumvented in the past by prior selection of a few transformed variables, using either principal component analysis or partial least squares. Although such selection ensures non-singularity of matrices, the decision process is arbitrary and valuable information on group structure may be lost. We therefore consider some ways of estimating linear discriminant functions without such prior selection. Several spectroscopic data sets are analysed with each method, and questions of bias of assessment procedures are investigated. All proposed methods seem worthy of consideration in practice.

AB - Currently popular techniques such as experimental spectroscopy and computer-aided molecular modelling lead to data having very many variables observed on each of relatively few individuals. A common objective is discrimination between two or more groups, but the direct application of standard discriminant methodology fails because of singularity of covariance matrices. The problem has been circumvented in the past by prior selection of a few transformed variables, using either principal component analysis or partial least squares. Although such selection ensures non-singularity of matrices, the decision process is arbitrary and valuable information on group structure may be lost. We therefore consider some ways of estimating linear discriminant functions without such prior selection. Several spectroscopic data sets are analysed with each method, and questions of bias of assessment procedures are investigated. All proposed methods seem worthy of consideration in practice.

U2 - 10.2307/2986198

DO - 10.2307/2986198

M3 - Journal article

VL - 44

SP - 101

EP - 115

JO - Journal of the Royal Statistical Society: Series C (Applied Statistics)

JF - Journal of the Royal Statistical Society: Series C (Applied Statistics)

SN - 0035-9254

IS - 1

ER -