Triad-LMF: a hierarchical low-rank multimodal fusion framework for robust cancer subtype classification using multi-omics data.

Cancer heterogeneity poses a major challenge for accurate molecular subtype classification. Conventional methods often fail to exploit complementary information across multiple omics modalities, leading to overfitting on high-dimensional data and limited representation of subtype heterogeneity. To address this, we propose Triad-LMF, a multi-omics integration framework based on low-rank multimodal fusion to improve classification accuracy. Triad-LMF harmonizes heterogeneous omics data and integrates information through a two-stage hierarchical fusion strategy. Local Pairwise Fusion and Global Triadic Fusion are combined via the Two-Feature and Three-Way LMF modules, enabling a gradual transition from local modality interactions to global feature integration. Experimental results show that Triad-LMF consistently outperforms existing methods. UMAP visualization confirms enhanced subtype separability, and SHAP-based analysis highlights biologically meaningful features. Across independent datasets, Triad-LMF demonstrates strong generalization, offering a robust and interpretable framework for multi-omics-driven cancer subtype classification.