Multivariate longitudinal data clustering with a copula kernel mixture model

Abstract

Many common clustering methods cannot be used for clustering multivariate longitudinal data when the covariance of random variables is a function of the time points. For this reason, a copula kernel mixture model (CKMM) is proposed for clustering such data. The CKMM is a finite mixture model that decomposes each mixture component’s joint density function into a copula and marginal distribution functions, where a Gaussian copula is used for its mathematical traceability. This thesis considers three scenarios: first, the CKMM is developed for balanced multivariate longitudinal data with known eigenfunctions; second, the CKMM is used to fit unbalanced data where trajectories are aligned on the time axis, and eigenfunctions are unknown; and lastly, a dynamic CKMM (DCKMM) is applied to unbalanced data where trajectories are misaligned, and eigenfunctions are unknown. Expectation-maximization type algorithms are used for parameter estimation. The performance of CKMM is demonstrated on both simulated and real data.