Linear Discriminant Analysis (LDA) based on auxiliary slicing for binary classification data

Linear Discriminant Analysis (LDA) is a foundational algorithm in the realm of machine learning specifically designed for classification tasks. While effective, LDA's limitation lies in its ability to only reduce the feature space to one dimension in binary classification scenarios. This can result in a loss of vital information from the predictor variables, impacting the model's predictive capabilities. To address this issue, this study introduces an enhanced discriminant analysis model leveraging auxiliary slicing. This novel approach not only removes the constraint of one-dimensional reduction post LDA through equidistant binning but also enhances the extraction of local information by introducing a continuous auxiliary response variable. Through simulation experiments and real data analysis, it is demonstrated that our proposed method outperforms the traditional LDA model in terms of prediction accuracy and robustness.