An Enhanced Projection Pursuit Tree Classifier with Visual Methods for Assessing Algorithmic Improvements

TL;DR

This paper introduces improvements to the projection pursuit tree classifier that enhance its ability to handle complex, high-dimensional, multi-class problems, supported by visual diagnostic tools and an interactive web application.

Contribution

It proposes algorithmic enhancements for better performance in complex scenarios and develops visual diagnostic methods to verify these improvements.

Findings

Enhanced classifier performs better on complex datasets

Visual diagnostics confirm the effectiveness of the improvements

Interactive tool facilitates exploration of classifier behavior

Abstract

This paper presents enhancements to the projection pursuit tree classifier and visual diagnostic methods for assessing their impact in high dimensions. The original algorithm uses linear combinations of variables in a tree structure where depth is constrained to be less than the number of classes -- a limitation that proves too rigid for complex classification problems. Our extensions improve performance in multi-class settings with unequal variance-covariance structures and nonlinear class separations by allowing more splits and more flexible class groupings in the projection pursuit computation. Proposing algorithmic improvements is straightforward; demonstrating their actual utility is not. We therefore develop two visual diagnostic approaches to verify that the enhancements perform as intended. Using high-dimensional visualization techniques, we examine model fits on benchmark datasets to assess whether the algorithm behaves as theorized. An interactive web application enables users to explore the behavior of both the original and enhanced classifiers under controlled scenarios. The enhancements are implemented in the R package PPtreeExt.