Projection in genomic analysis: A theoretical basis to rationalize tensor decomposition and principal component...

Area of Science:

• Bioinformatics
• Computational Biology
• Genomics

Background:

• Identifying differentially expressed genes is challenging due to small sample sizes and large numbers of genes.
• Conventional statistical tests for gene selection are highly sensitive to sample size, affecting P-value reliability.
• Unsupervised feature extraction methods like principal component analysis (PCA) and tensor decomposition (TD) show promise but lack clear mechanistic understanding.

Purpose of the Study:

• To elucidate the underlying reasons for the success of PCA- and TD-based unsupervised feature extraction (FE) in gene selection.
• To connect the effectiveness of PCA and TD in FE to the principles of projection pursuit (PP).
• To validate these findings using real-world biological datasets.

Main Methods:

• Applied projection pursuit (PP) to analyze datasets previously studied with PCA and TD.
• Investigated the relationship between singular value vectors from PCA/TD and optimal cluster centroids from K-means.
• Utilized gene order shuffling procedures to empirically assess P-value thresholds.

Main Results:

• Demonstrated a strong coincidence between projection pursuit (PP) and PCA/TD-based unsupervised FE results across three diverse datasets.
• Established an equivalence between the spaces spanned by singular value vectors and K-means cluster centroids.
• Empirically validated P-value thresholds, showing consistency between Gaussian distribution assumptions and gene order shuffling.

Conclusions:

• The success of PCA- and TD-based unsupervised FE in gene selection is rationalized through their connection to projection pursuit.
• This study provides a theoretical framework for understanding why these advanced methods outperform conventional statistical approaches.
• Findings are robustly supported by applications to kidney cancer biomarker discovery and COVID-19 drug discovery datasets.