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

Area of Science:

• Biomedical Data Science
• Statistical Learning
• Multivariate Analysis

Background:

• High-dimensional biomedical data possess complex structures (distributional, correlational) challenging traditional analysis.
• Examples include single-cell RNA-seq (count/sparse data), microbiome (phylogenetic relationships), and spatial transcriptomics (spatial correlations).
• Effective dimensionality reduction is crucial for extracting meaningful biological insights from such data.

Purpose of the Study:

• To provide a selected review of linear dimensionality reduction methods for structured biomedical data.
• To compare existing supervised and unsupervised methods within a unified low-rank-plus-noise model framework.
• To enhance researchers' understanding of the strengths and limitations of various structured dimensionality reduction techniques.

Main Methods:

• Review of existing linear dimensionality reduction methods.
• Theoretical and numerical comparisons of methods.
• Utilizing a unified framework based on low-rank-plus-noise models.

Main Results:

• Comparison of supervised and unsupervised dimensionality reduction methods for structured data.
• Identification of strengths and limitations of various techniques.
• Theoretical and numerical evaluations of method performance.

Conclusions:

• Structured dimensionality reduction is essential for analyzing complex biomedical data.
• A deeper understanding of method capabilities aids in selecting appropriate analytical tools.
• Future research directions are highlighted for advancing dimensionality reduction in this field.