Gaussian copula mixture models (GCMM) are the generalization of Gaussian Mixture models using the concept of copula. Its mathematical definition is given and the properties of likelihood function are studied in this paper. Based on these properties, extended Expectation Maximum algorithms are developed for estimating parameters for the mixture of copulas while marginal distributions corresponding to each component is estimated using separate nonparametric statistical methods. In the experiment, GCMM can achieve better goodness-of-fitting given the same number of clusters as GMM; furthermore, GCMM can utilize unsynchronized data on each dimension to achieve deeper mining of data.

翻译：高斯Copula混合模型（GCMM）是利用Copula概念对高斯混合模型的推广。本文给出其数学定义，并研究了似然函数的性质。基于这些性质，我们发展了扩展期望最大化算法用于估计Copula混合的参数，同时采用独立的非参数统计方法估计每个分量对应的边际分布。实验表明，在聚类数量与高斯混合模型（GMM）相同的条件下，GCMM能获得更优的拟合优度；此外，GCMM可利用各维度上的非同步数据实现更深层次的数据挖掘。