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

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.