BIDIMENSIONAL LINKED MATRIX FACTORIZATION FOR PAN-OMICS PAN-CANCER ANALYSIS.

Area of Science:

• Computational Biology
• Bioinformatics
• Statistical Genomics

Background:

• Modern applications increasingly require integrating multiple large data matrices with shared rows/columns.
• Pan-omics pan-cancer analysis, integrating multiple omics platforms across cancer types, has advanced understanding of molecular heterogeneity.
• Existing statistical methods are limited for analyzing bidimensionally linked matrices.

Purpose of the Study:

• To propose BIDIFAC+, a flexible method for simultaneous factorization and decomposition of variation across bidimensionally linked matrices.
• To extend the factorization of linked matrices beyond single-dimension linkage.
• To provide a statistically robust and unique decomposition method.

Main Methods:

• Developed BIDIFAC+, a novel approach for simultaneous factorization and decomposition.
• Utilized an objective function extending nuclear norm penalization, motivated by random matrix theory.
• Ensured a unique decomposition under mild conditions, aligning with Bayesian posterior distribution modes.

Main Results:

• Applied BIDIFAC+ to The Cancer Genome Atlas (TCGA) pan-omics data.
• Identified shared and specific modes of variability across four omics platforms.
• Analyzed data from 29 different cancer types, revealing complex interrelations.

Conclusions:

• BIDIFAC+ offers a powerful new tool for analyzing complex, multi-dimensional biological data.
• The method facilitates deeper understanding of molecular heterogeneity in cancer.
• Enables robust identification of shared and specific variability patterns in pan-omics studies.