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.

翻译：本文研究了高斯连接函数混合模型（GCMM），该模型是高斯混合模型（GMM）的扩展，融合了连接函数的概念。论文给出了GCMM的数学定义，并探讨了其似然函数的性质。此外，论文提出了扩展的期望最大化算法来估计连接函数混合模型的参数。每个成分对应的边缘分布采用非参数统计方法单独估计。实验表明，在使用相同聚类数量的情况下，GCMM相比GMM表现出更好的拟合优度。此外，GCMM能够利用各维度间不同步的数据，实现更全面的数据分析。