ci-fGBD: Cluster-Integrated Fast Generalized Bruhat Decomposition for Multimodal Data Clustering in Alzheimer's Disease.

Multimodal biomedical datasets, such as those from neurodegenerative disease cohorts, present significant challenges in stratifying heterogeneous patient populations due to missing values, high dimensionality, and modality-specific biases. Traditional clustering methods often require extensive preprocessing and fail to integrate heterogeneous data types effectively. We introduce ci-fGBD (Cluster-Integrated Fast Generalized Bruhat Decomposition), a novel matrix factorization and clustering framework that natively operates on block-structured, multimodal datasets. ci-fGBD extends the classical Bruhat decomposition by jointly learning latent representations and patient clusters while automatically harmonizing contributions across diverse modalities, including neuroimaging, cognitive assessments, genomics, wearable sensors, and environmental exposures. Benchmarking against standard methods on real datasets demonstrates that ci-fGBD consistently identifies clinically meaningful subgroups, capturing subtle biological, cognitive, and demographic heterogeneity in Alzheimers disease cohorts with superior interpretability and robustness.