Clustering Hybrid Functional and Vector Data.

Modern biomedical studies increasingly collect hybrid data, consisting of functional observations (e.g., curves or images) and multiple scalar (vector-valued) clinical variables. Integrating these modalities in an unsupervised learning framework can improve patient subgroup identification and interpretation, yet most existing clustering approaches handle only a single data type. We introduce a clustering framework for hybrid data combining multivariate functional and vector outcomes. The method first applies hybrid principal component analysis to capture joint mean structures and modes of variation across modalities, then iteratively reassigns subjects using a hybrid distance metric based on cluster-specific Karhunen-Loéve expansions. This approach accommodates multiple functions of varying dimensions, integrates contributions from functional and vector components in mean and covariance structures, and avoids parametric distributional assumptions. Simulation studies show that the proposed method outperforms competing approaches when subgroup information, in terms of mean and/or variance differences, is either distributed across modalities or concentrated in a single modality. We illustrate the method using renal radionuclide imaging data, including baseline and diuretic renogram curves and pharmacokinetic variables from patients with suspected kidney obstruction. The method identifies clinically meaningful subgroups consistent with expert assessment, demonstrating its potential to support data-driven decision-making in multimodal biomedical studies.