Contrastive Latent Functional Model.

Functional Principal Component Analysis (FPCA) is a popular tool for representing functional data in lower-dimensions, along highly-interpretable components depicting directions of variation in the data across time. We extend FPCA to contrastive settings involving multiple groups with a focus on time-dynamic components which are shared across samples versus those that are unique to a particular sample. The proposed Contrastive Latent Functional Model (cLFM) integrates FPCA with contrastive learning principles to capture common directions of variation across datasets while isolating distinct features specific to each sample. The model employs a computationally efficient Expectation-Maximization (EM) algorithm for parameter estimation, ensuring orthogonality between shared and unique functional spaces. Simulation studies demonstrate the efficacy of the proposed method across different scenarios of shared and unique variation, varying sample size and error variance. Applied to neurodevelopmental and clinical datasets, including EEG studies and longitudinal studies of kidney function, cLFM reveals novel insights into group differences between autism vs neurotypical development and among mild to severe albuminuria subgroups of chronic kidney disease patients. Bridging contrastive analysis with functional data, this framework advances the capacity to disentangle complex variation patterns in multi-group functional studies in biomedical research.