09: Clustering of functional data prone to complex heteroscedastic measurement error

Music City Center 

Several factors make clustering functional data challenging, including the infinite dimensional space to which observations belong and the lack of a defined probability density function for functional random variables. Despite extensive literature describing clustering methods for functional data, clustering of error-prone functional data remains poorly explored. We propose a two-stage approach: first, clustered mixed-effects models are applied to adjust for measurement-error bias; second, cluster analysis is applied to measurement error–adjusted curves. Readily available methods (e.g., K-means, mclust) can be used to perform the cluster analysis. We use simulations to examine how complex heteroscedastic measurement error affects clustering, considering variations in sample sizes, error magnitudes, and correlation structures. Our results show that ignoring measurement error in functional data reduces the accuracy of identifying true latent clusters. When applied to a school-based study of energy expenditure among elementary school–aged children in Texas, our methods achieved enhanced clustering of energy expenditure.

clustering

functional data

measurement error

physical activity

wearable device 

Biometrics Section