A Convex formulation for linear discriminant analysis

The recent surge in multisource data collection has drastically increased data dimensionality, particularly in omics analysis, where gene expression data from microarrays or nextgeneration sequencing can exceed 50,000 measurements [32]. High-dimensional datasets often contain noisy, redundant, missing, or irrelevant features, which can degrade the performance of pattern recognition tasks [28]. The acquisition of such high-dimensional datasets necessitates innovative techniques that can effectively handle large-scale data while remaining robust to noise [30]. DR is widely applied as an essential step to extract meaningful features enabling more effective data visualization, feature extraction, and improved downstream predictive performance [12, 24]. With the advent of deep neural networks (DNNs) such as large language models (LLMs), convolutional neural networks (CNNs), and transformers, DR techniques may seem less prominent. However, despite the success of these complex architectures, linear dimensionality reduction remains a powerful and practical approach due to its interpretability, computational efficiency, and robustness in high-dimensional, low-sample-size (HDLSS) regimes [28]. Deep learning models excel at learning hierarchical representations but pose significant challenges. They require large amounts of labeled data, extensive hyper-parameter tuning, and substantial computational resources. Additionally, these models often function as black boxes, offering little interpretability of their decision-making processes [26].