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General sparse multi-class linear discriminant analysis

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  • Safo, Sandra E.
  • Ahn, Jeongyoun

Abstract

Discrimination with high dimensional data is often more effectively done with sparse methods that use a fraction of predictors rather than using all the available ones. In recent years, some effective sparse discrimination methods based on Fisher’s linear discriminant analysis (LDA) have been proposed for binary class problems. Extensions to multi-class problems are suggested in those works; however, they have some drawbacks such as the heavy computational cost for a large number of classes. We propose an approach to generalize a binary LDA solution into a multi-class solution while avoiding the limitations of the existing methods. Simulation studies with various settings, as well as real data examples including next generation sequencing data, confirm the effectiveness of the proposed approach.

Suggested Citation

  • Safo, Sandra E. & Ahn, Jeongyoun, 2016. "General sparse multi-class linear discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 81-90.
    • Handle: RePEc:eee:csdana:v:99:y:2016:i:c:p:81-90
    DOI: 10.1016/j.csda.2016.01.011
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    1. Brenton R. Graveley & Angela N. Brooks & Joseph W. Carlson & Michael O. Duff & Jane M. Landolin & Li Yang & Carlo G. Artieri & Marijke J. van Baren & Nathan Boley & Benjamin W. Booth & James B. Brown , 2011. "The developmental transcriptome of Drosophila melanogaster," Nature, Nature, vol. 471(7339), pages 473-479, March.
    2. Jeongyoun Ahn & J. S. Marron, 2010. "The maximal data piling direction for discrimination," Biometrika, Biometrika Trust, vol. 97(1), pages 254-259.
    3. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    4. Qing Mai & Hui Zou & Ming Yuan, 2012. "A direct approach to sparse discriminant analysis in ultra-high dimensions," Biometrika, Biometrika Trust, vol. 99(1), pages 29-42.
    5. Lee, Yoonkyung & Lin, Yi & Wahba, Grace, 2004. "Multicategory Support Vector Machines: Theory and Application to the Classification of Microarray Data and Satellite Radiance Data," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 67-81, January.
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    Cited by:

    1. Elżbieta Szaruga & Elżbieta Skąpska & Elżbieta Załoga & Wiesław Matwiejczuk, 2018. "Trust and Distress Prediction in Modal Shift Potential of Long-Distance Road Freight in Containers: Modeling Approach in Transport Services for Sustainability," Sustainability, MDPI, vol. 10(7), pages 1-19, July.
    2. 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.
    3. Li-Pang Chen & Grace Y. Yi & Qihuang Zhang & Wenqing He, 2019. "Multiclass analysis and prediction with network structured covariates," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-25, December.
    4. Hirose, Kei & Miura, Kanta & Koie, Atori, 2023. "Hierarchical clustered multiclass discriminant analysis via cross-validation," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    5. Li-Pang Chen, 2022. "Network-Based Discriminant Analysis for Multiclassification," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 410-431, November.

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