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.