The Rayleigh Quotient and Contrastive Principal Component Analysis I

Area of Science:

• Genomics
• Bioinformatics
• Computational Biology

Background:

• Contrastive learning is valuable for identifying genomic signals and reducing noise.
• Contrastive PCA is a popular method but struggles with scalability for large datasets.

Purpose of the Study:

• To introduce rho PCA, a novel method that addresses the scalability limitations of contrastive PCA.
• To demonstrate the accuracy and efficiency of rho PCA compared to existing methods.

Main Methods:

• The study shows the contrastive PCA objective approximates a Rayleigh quotient, termed rho PCA.
• Utilized generalized eigenvectors for interpretable dimension reduction.
• Applied rho PCA to single-nucleus transcriptomics data for contrasting conditions.

Main Results:

• Rho PCA is more accurate and significantly more efficient than contrastive PCA.
• Demonstrated rho PCA's utility for dimension reduction with controls and contrasting experimental conditions.
• Provided probabilistic interpretations offering insights into rho PCA's performance.

Conclusions:

• Rho PCA offers a scalable, accurate, and interpretable alternative to contrastive PCA for genomic data analysis.
• The method is versatile, applicable to various dimension reduction tasks including single-nucleus transcriptomics.
• Probabilistic interpretations enhance understanding of rho PCA's effectiveness.