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

• URL: http://arxiv.org/abs/2409.03136v1
• Date: Thu, 5 Sep 2024 00:12:15 GMT
• Title: A New Forward Discriminant Analysis Framework Based On Pillai's Trace and ULDA
• Authors: Siyu Wang,
• Abstract summary: This paper introduces a novel forward discriminant analysis framework that integrates Pillai's trace with Uncorrelated Linear Discriminant Analysis (ULDA) to address these challenges. Through simulations and real-world datasets, the new framework demonstrates effective control of Type I error rates and improved classification accuracy.
• Score: 6.087464679182875
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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