Informational rescaling of PCA maps with application to genetic distance

Area of Science:

• Multivariate data analysis
• Bioinformatics
• Information theory

Background:

• Principal Component Analysis (PCA) is widely used for data dimensionality reduction.
• Interpreting distances in low-dimensional PCA projections remains a challenge.
• Genomic data analysis often involves complex, high-dimensional datasets.

Purpose of the Study:

• To propose a novel heuristic for transforming PCA maps into entropy-based maps.
• To enhance the interpretability of distances in PCA projections using mutual information (MI).
• To demonstrate the utility of this method for improving cluster identification, particularly in genomic data.

Main Methods:

• Developed a computationally simple heuristic to rescale PCA.
• Utilized mutual information (MI) to transform standard PCA distances into entropy-based distances.
• Applied the entropy-rescaled PCA to genomic data from world populations.

Main Results:

• The proposed method transforms PCA maps into entropy-based maps where distances reflect mutual information.
• Entropy-rescaled PCA can improve cluster identification in certain datasets.
• Distances are quantified in information units (e.g., bits), representing relative statistical associations.

Conclusions:

• Entropy-rescaled PCA offers a more interpretable way to analyze high-dimensional data, especially in genetics.
• The method preserves order relationships while providing distances in meaningful information units.
• This approach enhances the understanding of genomic mutual information across populations.