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Multiclass Sparse Discriminant Analysis Incorporating Graphical Structure Among Predictors

Author

Listed:
  • Jingxuan Luo

    (Beijing Normal University)

  • Xuejiao Li

    (Beijing University of Technology)

  • Chongxiu Yu

    (Beijing University of Technology)

  • Gaorong Li

    (Beijing Normal University)

Abstract

In the era of big data, many sparse linear discriminant analysis methods have been proposed for classification and variable selection of the high-dimensional data. In order to solve the multiclass sparse discriminant problem for high-dimensional data under the Gaussian graphical model, this paper proposes a multiclass sparse discrimination analysis method by incorporating the graphical structure among predictors, which is named as IG-MSDA method. Our proposed IG-MSDA method can be used to estimate the vectors of all discriminant directions simultaneously. Under certain regularity conditions, it is shown that the proposed IG-MSDA method can consistently estimate all discriminant directions and the Bayes rule. Further, we establish the convergence rates of the estimators for the discriminant directions and the conditional misclassification rates. Finally, simulation studies and a real data analysis demonstrate the good performance of our proposed IG-MSDA method.

Suggested Citation

  • Jingxuan Luo & Xuejiao Li & Chongxiu Yu & Gaorong Li, 2023. "Multiclass Sparse Discriminant Analysis Incorporating Graphical Structure Among Predictors," Journal of Classification, Springer;The Classification Society, vol. 40(3), pages 614-637, November.
    • Handle: RePEc:spr:jclass:v:40:y:2023:i:3:d:10.1007_s00357-023-09451-1
    DOI: 10.1007/s00357-023-09451-1
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