# Structural Effect and Spectral Enhancement of High-Dimensional Regularized Linear Discriminant Analysis

arXiv: https://arxiv.org/abs/2507.16682 · HTML: https://mlsanity.com/paper/2507.16682/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 38 references that are in the map.
- First posted on arXiv 22 Jul 2025.

## Builds on (most cited first, 5 of 5)

- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [High-Dimensional Asymptotics of Prediction: Ridge Regression and Classification](https://mlsanity.com/paper/1507.03003/) (2015)
- [High-dimensional Ordinary Least-squares Projection for Screening Variables](https://mlsanity.com/paper/1506.01782/) (2015)
- [Generalized Four Moment Theorem and an Application to CLT for Spiked Eigenvalues of Large-dimensional Covariance Matrices](https://mlsanity.com/paper/1808.05362/) (2018)
- [A universal test on spikes in a high-dimensional generalized spiked model and its applications](https://mlsanity.com/paper/2203.06924/) (2022)

## Built on by (most cited first, 1 of 1)

- [Transfer Learning for Linear Discriminant Analysis with a Shared Classification Signal](https://mlsanity.com/paper/2607.06936/) (2026)

## Abstract (arXiv)

Regularized linear discriminant analysis (RLDA) is a widely used tool for classification and dimensionality reduction, but its performance in high-dimensional scenarios is inconsistent. Existing theoretical analyses of RLDA often lack clear insight into how data structure affects classification performance. To address this issue, we derive a non-asymptotic approximation of the misclassification rate and thus analyze the structural effect and structural adjustment strategies of RLDA. Based on this, we propose the Spectral Enhanced Discriminant Analysis (SEDA) algorithm, which optimizes the data structure by adjusting the spiked eigenvalues of the population covariance matrix. By developing a new theoretical result on eigenvectors in random matrix theory, we derive an asymptotic approximation on the misclassification rate of SEDA. The bias correction algorithm and parameter selection strategy are then obtained. Experiments on synthetic and real datasets show that SEDA achieves higher classification accuracy and dimensionality reduction compared to existing LDA methods.