Multiomics-Based Tensor Decomposition for Characterizing Breast Cancer Heterogeneity

Breast cancer is heterogeneous and consists of intrinsic components with various alterations. Combining multiple genomic sources to identify the intrinsic components and their heterogeneity is essential for precise clinical decision-making. In this chapter, we first described the breast cancer heterogeneity, then showed the principles of tensor and Bayesian tensor factorization, finally showed an example to explore the heterogenous intrinsic hallmarks of breast cancer by decomposing the integrated tensor of gene expression, copy number alteration, and DNA methylation information. This is achieved by using advanced tensor decomposition, which can extract multi-level latent representatives for both patients and genes. Gene set enrichment analysis were applied to estimate the key biological functions of the identified intrinsic genomic components. Patient stratification and survival analysis were performed based on the heterogeneity of these functional genomic components. The findings were evaluated using The Cancer Genome Atlas Breast Carcinoma (TCGA-BRCA) dataset. The analyses provide insight into how multiomics can identify functional intrinsic components of cancer and stratify patients into prognostically significant groups.