Machine Learning‐Enhanced Random Matrix Theory Design for Human Immunodeficiency Virus Vaccine Development

Human immunodeficiency virus (HIV)'s rapid evolution and immune evasion present significant challenges for vaccine designers, as identifying potential targets needs to differentiate adaptive mutations from random noise. Conventional methods tend to ignore the statistical rigor required to distinguish between hypervariable epitopes that are vulnerable to immunological escape and biologically specific regions, which are crucial for viral fitness. Random matrix theory (RMT) aids in identifying key correlations in complex biological data to enhance the selection of vaccine targets but faces challenges in accurately estimating covariance matrices when dealing with limited samples. For small datasets, the highly correlated variables given by RMT may be misleading as the number of correlated occurrences may be too small. Principal component analysis (PCA) analysis is used here to validate the RMT results. This article presents an integrated approach supporting RMT with PCA to address these challenges. We demonstrate that utilizing PCA can validate RMT results enhancing the validity and reliability of analysis in cases where small sample sizes and high dimensions are present. We explored the utility of RMT in identifying correlated regions of protein sequences used for the development of an HIV vaccine. To validate, PCA was used to analyze whether the highly correlated variables given by RMT have high variations. The outcomes revealed a noteworthy alignment of about 89% of predicted correlated features with our predefined validation criteria, accompanied by a margin of error of about 11%. This emphasizes the efficacy of PCA in verifying RMT outcomes, highlighting its utility in enhancing the reliability and interpretability in case of limited datasets.