JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1096 10.6339/23-JDS1096 Computing in Data Science Assessment of Projection Pursuit Index for Classifying High Dimension Low Sample Size Data in R WuZhaoxing1 https://orcid.org/0000-0002-3153-2662 ZhangChunmingcmzhang@stat.wisc.edu1∗ University of Wisconsin-Madison, Department of Statistics, U.S.A. Corresponding author. Email: cmzhang@stat.wisc.edu. 2023232023212310332 Supplementary Material

All of our code is open source in the following GitHub repository https://github.com/zwu363/projection-pursuit-index.

71120222722023 2023 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2023 Open access article under the CC BY license.

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 ( PDA) index, built upon the Linear Discriminant Analysis ( 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 ( SVM). This paper conducts extensive numerical studies to compare the performance of the PDA index with the LDA index and SVM, demonstrating that the 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 PDA index provides a useful alternative tool for classifying complex high-dimensional data. These new insights, along with the hands-on implementation of the PDA index functions in the R package classPP, facilitate statisticians and data scientists to make effective use of both sets of classification tools.

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