  This paper investigates Gaussian copula mixture models (GCMM), which are an
extension of Gaussian mixture models (GMM) that incorporate copula concepts.
The paper presents the mathematical definition of GCMM and explores the
properties of its likelihood function. Additionally, the paper proposes
extended Expectation Maximum algorithms to estimate parameters for the mixture
of copulas. The marginal distributions corresponding to each component are
estimated separately using nonparametric statistical methods. In the
experiment, GCMM demonstrates improved goodness-of-fitting compared to GMM when
using the same number of clusters. Furthermore, GCMM has the ability to
leverage un-synchronized data across dimensions for more comprehensive data
analysis.
