Integrating Hypertension Phenotype and Genotype with Hybrid Non-negative Matrix Factorization

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.