  In this study, we introduce an innovative methodology aimed at enhancing
Fisher's Linear Discriminant Analysis (LDA) in the context of high-dimensional
data classification scenarios, specifically addressing situations where each
feature exhibits distinct variances. Our approach leverages Nonparametric
Maximum Likelihood Estimation (NPMLE) techniques to estimate both the mean and
variance parameters. By accommodating varying variances among features, our
proposed method leads to notable improvements in classification performance. In
particular, unlike numerous prior studies that assume the distribution of
heterogeneous variances follows a right-skewed inverse gamma distribution, our
proposed method demonstrates excellent performance even when the distribution
of heterogeneous variances takes on left-skewed, symmetric, or right-skewed
forms. We conducted a series of rigorous experiments to empirically validate
the effectiveness of our approach. The results of these experiments demonstrate
that our proposed methodology excels in accurately classifying high-dimensional
data characterized by heterogeneous variances.
