Unbalanced Longitudinal Data Clustering with a Copula Kernel Mixture Model - Zhang, Xi; Murphy, Orla A.; McNicholas, Paul D. (Statistics and computing, 2025)
Unbalanced longitudinal data appears commonly in practice, for example in cases where measurements are collected at different time points for different subjects and can therefore be sparse and/or irregularly sampled. Treating such data as functional enables smooth curve estimation and better handling of missing or irregularly spaced observations. Therefore, a Gaussian copula kernel mixture model (CKMM), based on functional data analysis, is proposed for clustering unbalanced multivariate longitudinal data. In this model, subject-specific warping matrices are included to account for irregularly spaced observations. A regularized functional eigen-decomposition is employed to estimate the copula correlation parameters, ensuring the smoothing procedure is integrated into clustering. Additionally, a functional gradient descent algorithm is implemented as an alternative to kernel density estimation to reduce computational complexity. An expectation-maximization-like algorithm is proposed to estimate marginal distributions, copula parameters, eigenfunctions, and eigenvalues in the CKMM. The performance of the CKMM is demonstrated through a simulation study and a data application. The proposed model exhibits superior performance compared to k-means with dynamic time warping, the growth mixture model, and functional high-dimensional data clustering.