X-intNMF: A Cross- and Intra-Omics Regularized NMF Framework for Multi-Omics Integration

Motivation: The rapid accumulation of multi-omics data presents a valuable opportunity to advance our understanding of complex diseases and biological systems, driving the development of integrative computational methods. However, the complexity of biological processes - spanning multiple molecular layers and involving intricate regulatory interactions - requires models that can capture both intra- and cross-omics relationships. Most existing integration methods primarily focus on sample-level similarities or intra-omics feature interactions, often neglecting the interactions across different omics layers. This limitation can result in the loss of critical biological information and suboptimal performance. To address this gap, we propose X-intNMF, a network-regularized non-negative matrix factorization (NMF) model that explicitly incorporates both cross-omics and intra-omics feature interaction networks during multi-omics integration. By modeling these multi-layered relationships, X-intNMF enhances the representation of biological interactions and improves integration quality and prediction accuracy. Results: For evaluation, we applied X-intNMF to predict breast cancer phenotypes and classify clinical outcomes in lung and ovarian cancers using mRNA expression, microRNA expression, and DNA methylation data from TCGA. The results show that X-intNMF consistently outperforms state-of-the-art methods. Ablation studies confirm that incorporating both cross-omics and intra-omics interactions contributes significantly to the model's improved performance. Additionally, survival analysis demonstrates that the integrated multi-omics representation offers strong prognostic value for both overall survival and disease-free status. These findings highlight X-intNMF's ability to effectively model multi-layered molecular interactions while maintaining interpretability, robustness, and scalability within the NMF framework.