  Hypertension is a heterogeneous syndrome in need of improved subtyping using
phenotypic and genetic measurements so that patients in different subtypes
share similar pathophysiologic mechanisms and respond more uniformly to
targeted treatments. Existing machine learning approaches often face challenges
in integrating phenotype and genotype information and presenting to clinicians
an interpretable model. We aim to provide informed patient stratification by
introducing Hybrid Non-negative Matrix Factorization (HNMF) on phenotype and
genotype matrices. HNMF simultaneously approximates the phenotypic and genetic
matrices using different appropriate loss functions, and generates patient
subtypes, phenotypic groups and genetic groups. Unlike previous methods, HNMF
approximates phenotypic matrix under Frobenius loss, and genetic matrix under
Kullback-Leibler (KL) loss. We propose an alternating projected gradient method
to solve the approximation problem. Simulation shows HNMF converges fast and
accurately to the true factor matrices. On real-world clinical dataset, we used
the patient factor matrix as features to predict main cardiac mechanistic
outcomes. We compared HNMF with six different models using phenotype or
genotype features alone, with or without NMF, or using joint NMF with only one
type of loss. HNMF significantly outperforms all comparison models. HNMF also
reveals intuitive phenotype-genotype interactions that characterize cardiac
abnormalities.
