Latent Structure in Ehr Data: Reconstruction of Diabetes Markers with Sparse NMF

The dimensionality of electronic health record (EHR) data continues to grow as more clinical variables are recorded, often resulting in redundancy, sparsity, and analytical intractability. In this study, we apply non-negative matrix factorization (NMF) to a high-dimensional laboratory dataset of patients with type II diabetes to estimate the minimum latent dimensionality required to preserve clinically meaningful information. Using both within-patient imputation and across-patient generalization tasks, we evaluate the ability of the learned representations to reconstruct two key clinical lab values: blood glucose and HbA1c. Our findings show that clinically acceptable accuracy can be achieved with a dimensionality reduction of up to 80% and a dimensionality of 230 to 300, supporting the presence of a compact, low-dimensional latent structure underlying high-dimensional clinical data.