A New Forward Discriminant Analysis Framework Based On Pillai's Trace and ULDA

Siyu Wang; Kehui Yao

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arXiv · 2409.03136

A New Forward Discriminant Analysis Framework Based On Pillai's Trace and ULDA

Siyu Wang·Kehui Yao

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Abstract

Linear discriminant analysis (LDA), a traditional classification tool, suffers from limitations such as sensitivity to noise and computational challenges when dealing with non-invertible within-class scatter matrices. Traditional stepwise LDA frameworks, which iteratively select the most informative features, often exacerbate these issues by relying heavily on Wilks' $\Lambda$, potentially causing premature stopping of the selection process. This paper introduces a novel forward discriminant analysis framework that integrates Pillai's trace with Uncorrelated Linear Discriminant Analysis (ULDA) to address these challenges, and offers a unified and stand-alone classifier. Through simulations and real-world datasets, the new framework demonstrates effective control of Type I error rates and improved classification accuracy, particularly in cases involving perfect group separations. The results highlight the potential of this approach as a robust alternative to the traditional stepwise LDA framework.

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Siyu Wang, Kehui Yao. 2024-09-05. A New Forward Discriminant Analysis Framework Based On Pillai's Trace and ULDA. https://arxiv.org/abs/2409.03136

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