Longitudinal Data Clustering Via Kernel Mixture Models

Abstract

Kernel mixture models are proposed to cluster univariate, independent multivariate and dependent bivariate longitudinal data. The Gaussian distribution in finite mixture models is replaced by the Gaussian and gamma kernel functions, and the expectation-maximization algorithm is used to estimate bandwidths and compute log-likelihood scores. For dependent bivariate longitudinal data, the bivariate Gaussian copula is used to reveal the correlation between two attributes. After that, we use AIC, BIC and ICL to select the best model. In addition, we also introduce a kernel distance-based clustering method to compare with the kernel mixture models. A simulation is performed to illustrate the performance of this mixture model, and results show that the gamma kernel mixture model performs better than the kernel distance-based clustering method based on misclassification rates. Finally, these two models are applied to COVID-19 data, and sixty countries are classified into ten clusters based on growth rates and death rates.