ULSL: Unified Latent and Similarity Learning for robust multi-omics cancer subtype identification.

Motivation: Cancer's high heterogeneity necessitates precise molecular classification for improved clinical outcomes. However, current multi-omics clustering often struggles with molecular complexity. We propose Unified Latent and Similarity Learning (ULSL), a novel framework that simultaneously learns latent embeddings and similarity matrices through unified optimization. ULSL employs graph fusion for cross-omics structural consistency and latent representation learning to project data into low-dimensional spaces, effectively mitigating noise and high dimensionality. Results: ULSL was evaluated on synthetic datasets and 10 public cancer datasets from The Cancer Genome Atlas (TCGA). It consistently outperformed seven state-of-the-art methods in accuracy and robustness for subtype identification. On simulated datasets, ULSL maintained superior performance even with weak signal features and high noise levels. On TCGA datasets, ULSL not only identified survival-associated subtypes in a larger number of cancer types but also detected a greater number of clinically enriched features compared to competing approaches. Furthermore, the specific case study on AML demonstrated that ULSL aligns with the biological basis of the traditional FAB classification while offering distinct advantages in prognostic stratification. Availability and implementation: The source code for ULSL is available at https://github.com/codelzy-01/ULSL-1.git.