Linear Dimensionality Reduction Methods for Analyzing Structured Biomedical Data: Existing Research and Future Opportunities

High-dimensional biomedical data often exhibit complex structural features that challenge traditional analytical methods. These features include distributional structures, such as count and sparse data in single-cell RNA-seq studies; correlation structures among biomarkers, such as phylogenetic relationships in microbiome studies; and correlation structures among samples, such as spatial correlations in spatial transcriptomics. Dimensionality reduction methods that account for these structures are essential for extracting biologically meaningful insights. This article provides a selected review of existing linear dimensionality reduction methods for both supervised and unsupervised analysis of structured data. Leveraging a unified framework based on low-rank-plus-noise models, we conduct theoretical and numerical comparisons of these methods. Our review aims to equip researchers with a deeper understanding of the strengths and limitations of various structured dimensionality reduction techniques, aiding in the selection of the most suitable approach for their data. Finally, this review highlights several promising directions for future research, offering opportunities for advancements in dimensionality reduction methods tailored to the unique complexities of structured biomedical data. This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Modeling MethodsStatistical and Graphical Methods of Data Analysis > Multivariate AnalysisStatistical and Graphical Methods of Data Analysis > Dimension Reduction.