Bidimensional linked matrix factorization for pan-omics pan-cancer analysis
This addresses the limitation in statistical methodology for cancer studies integrating multiple omics platforms and cancer types, though it appears incremental as it builds on existing linked matrix factorization literature.
The authors tackled the problem of integrating multiple large data matrices with shared rows and columns, such as in pan-omics pan-cancer analysis, by proposing BIDIFAC+, a flexible factorization method that decomposes variation into low-rank components shared across omics platforms and cancer types, applied to TCGA data across 4 omics platforms and 29 cancer types.
Several modern applications require the integration of multiple large data matrices that have shared rows and/or columns. For example, cancer studies that integrate multiple omics platforms across multiple types of cancer, pan-omics pan-cancer analysis, have extended our knowledge of molecular heterogenity beyond what was observed in single tumor and single platform studies. However, these studies have been limited by available statistical methodology. We propose a flexible approach to the simultaneous factorization and decomposition of variation across such bidimensionally linked matrices, BIDIFAC+. This decomposes variation into a series of low-rank components that may be shared across any number of row sets (e.g., omics platforms) or column sets (e.g., cancer types). This builds on a growing literature for the factorization and decomposition of linked matrices, which has primarily focused on multiple matrices that are linked in one dimension (rows or columns) only. Our objective function extends nuclear norm penalization, is motivated by random matrix theory, gives an identifiable decomposition under relatively mild conditions, and can be shown to give the mode of a Bayesian posterior distribution. We apply BIDIFAC+ to pan-omics pan-cancer data from TCGA, identifying shared and specific modes of variability across 4 different omics platforms and 29 different cancer types.