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Modified linear discriminant analysis approaches for classification of high-dimensional microarray data

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  • Xu, Ping
  • Brock, Guy N.
  • Parrish, Rudolph S.

Abstract

Linear discriminant analysis (LDA) is one of the most popular methods of classification. For high-dimensional microarray data classification, due to the small number of samples and large number of features, classical LDA has sub-optimal performance corresponding to the singularity and instability of the within-group covariance matrix. Two modified LDA approaches (MLDA and NLDA) were applied for microarray classification and their performance criteria were compared with other popular classification algorithms across a range of feature set sizes (number of genes) using both simulated and real datasets. The results showed that the overall performance of the two modified LDA approaches was as competitive as support vector machines and other regularized LDA approaches and better than diagonal linear discriminant analysis, k-nearest neighbor, and classical LDA. It was concluded that the modified LDA approaches can be used as an effective classification tool in limited sample size and high-dimensional microarray classification problems.

Suggested Citation

  • Xu, Ping & Brock, Guy N. & Parrish, Rudolph S., 2009. "Modified linear discriminant analysis approaches for classification of high-dimensional microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1674-1687, March.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:5:p:1674-1687
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    2. Brendan P. W. Ames & Mingyi Hong, 2016. "Alternating direction method of multipliers for penalized zero-variance discriminant analysis," Computational Optimization and Applications, Springer, vol. 64(3), pages 725-754, July.
    3. Frénay, Benoît & Doquire, Gauthier & Verleysen, Michel, 2014. "Estimating mutual information for feature selection in the presence of label noise," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 832-848.
    4. Sung, Bongjung & Lee, Jaeyong, 2023. "Covariance structure estimation with Laplace approximation," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    5. Ruiyan Luo & Xin Qi, 2017. "Asymptotic Optimality of Sparse Linear Discriminant Analysis with Arbitrary Number of Classes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 598-616, September.
    6. Michael Fop & Pierre-Alexandre Mattei & Charles Bouveyron & Thomas Brendan Murphy, 2022. "Unobserved classes and extra variables in high-dimensional discriminant analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(1), pages 55-92, March.
    7. Shen, Yanfeng & Lin, Zhengyan & Zhu, Jun, 2011. "Shrinkage-based regularization tests for high-dimensional data with application to gene set analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2221-2233, July.
    8. A. Poterie & J.-F. Dupuy & V. Monbet & L. Rouvière, 2019. "Classification tree algorithm for grouped variables," Computational Statistics, Springer, vol. 34(4), pages 1613-1648, December.
    9. Ivana Krtolica & Dragan Savić & Bojana Bajić & Snežana Radulović, 2022. "Machine Learning for Water Quality Assessment Based on Macrophyte Presence," Sustainability, MDPI, vol. 15(1), pages 1-13, December.
    10. Pires, Ana M. & Branco, João A., 2010. "Projection-pursuit approach to robust linear discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2464-2485, November.
    11. Parrish, Rudolph S. & Spencer III, Horace J. & Xu, Ping, 2009. "Distribution modeling and simulation of gene expression data," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1650-1660, March.
    12. Pedro Duarte Silva, A., 2011. "Two-group classification with high-dimensional correlated data: A factor model approach," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2975-2990, November.
    13. Kubokawa, Tatsuya & Hyodo, Masashi & Srivastava, Muni S., 2013. "Asymptotic expansion and estimation of EPMC for linear classification rules in high dimension," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 496-515.

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