Diagonal Multi-omics Integration of Heterogeneous Datasets

In this paper, we consider methods for the diagonal multi-omics integration of heterogeneous datasets. Several approaches to the nature of biological heterogeneity are analyzed and developed to comprehend more clearly the generated differences. Specifically, the extremal trace problems for the coupled Laplacian on sets homeomorphic to the Stiefel manifold embedded in the complex Euclidean space are investigated. The gradient ascent method for the maximization problem is elaborated in the classical terms of functional analysis, which is of significant interest in itself. On this basis, we introduce a novel characteristic of dataset heterogeneity by employing the norm of the difference between the maximum and minimum points.

CMGL: Confidence-guided Multi-omics Graph Learning for Cancer Subtype Classification

Motivation: Multi-omics integration can improve cancer subtyping, but modality informativeness and noise vary across cancer types and patients. Existing graph-based methods optimize modality weights jointly with the classification objective and therefore lack independent reliability estimates, so low-quality omics distort patient similarity graphs and amplify noise through message passing. Results: We propose CMGL, a two-stage framework that estimates per-sample modality reliability through evidential deep learning and uses the frozen confidence scores to guide cross-omics fusion and graph construction. On four MLOmics cancer-subtype tasks and the 32-class pan-cancer task, CMGL consistently improves over the strongest baseline, surpassing it by 4.03% in average accuracy on the four single-cancer tasks. Its representations recover the PAM50 intrinsic subtypes of breast invasive carcinoma (BRCA), and the BRCA-trained model transfers without fine-tuning to kidney renal clear cell carcinoma (KIRC), stratifying patients into prognostically distinct groups.