Assessment of Projection Pursuit Index for Classifying High Dimension Low Sample Size Data in R
Volume 21, Issue 2 (2023): Special Issue: Symposium Data Science and Statistics 2022, pp. 310–332
Pub. online: 2 March 2023
Type: Computing In Data Science
Open Access
Open Access
Received
7 November 2022
7 November 2022
Accepted
27 February 2023
27 February 2023
Published
2 March 2023
2 March 2023
Abstract
Analyzing “large p small n” data is becoming increasingly paramount in a wide range of application fields. As a projection pursuit index, the Penalized Discriminant Analysis ($\mathrm{PDA}$) index, built upon the Linear Discriminant Analysis ($\mathrm{LDA}$) index, is devised in Lee and Cook (2010) to classify high-dimensional data with promising results. Yet, there is little information available about its performance compared with the popular Support Vector Machine ($\mathrm{SVM}$). This paper conducts extensive numerical studies to compare the performance of the $\mathrm{PDA}$ index with the $\mathrm{LDA}$ index and $\mathrm{SVM}$, demonstrating that the $\mathrm{PDA}$ index is robust to outliers and able to handle high-dimensional datasets with extremely small sample sizes, few important variables, and multiple classes. Analyses of several motivating real-world datasets reveal the practical advantages and limitations of individual methods, suggesting that the $\mathrm{PDA}$ index provides a useful alternative tool for classifying complex high-dimensional data. These new insights, along with the hands-on implementation of the $\mathrm{PDA}$ index functions in the R package classPP, facilitate statisticians and data scientists to make effective use of both sets of classification tools.
Supplementary material
Supplementary MaterialAll of our code is open source in the following GitHub repository https://github.com/zwu363/projection-pursuit-index.
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