Longitudinal Data Clustering with a Copula Kernel Mixture Model

TL;DR

This paper introduces a copula kernel mixture model (CKMM) for clustering multivariate longitudinal data with high autocorrelations, effectively outperforming standard methods like K-means with dynamic time warping.

Contribution

The paper proposes a novel CKMM that decomposes joint densities into copula and marginal distributions, using Gaussian copulas and kernels, with a generalized EM algorithm for parameter estimation.

Findings

CKMM outperforms K-means with dynamic time warping.

CKMM performs well on simulated and real datasets.

The model effectively captures autocorrelated longitudinal data.

Abstract

Many common clustering methods cannot be used for clustering multivariate longitudinal data in cases where variables exhibit high autocorrelations. In this article, a copula kernel mixture model (CKMM) is proposed for clustering data of this type. The CKMM is a finite mixture model which decomposes each mixture component's joint density function into its copula and marginal distribution functions. In this decomposition, the Gaussian copula is used due to its mathematical tractability and Gaussian kernel functions are used to estimate the marginal distributions. A generalized expectation-maximization algorithm is used to estimate the model parameters. The performance of the proposed model is assessed in a simulation study and on two real datasets. The proposed model is shown to have effective performance in comparison to standard methods, such as K-means with dynamic time warping clustering and latent growth models.