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Extending mixtures of multivariate /-factor analyzers

机译：扩展多元/因子分析仪的混合物

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Model-based clustering typically involves the development of a family of mixture models and the imposition of these models upon data. The best member of the family is then chosen using some criterion and the associated parameter estimates lead to predicted group memberships, or clusterings. This paper describes the extension of the mixtures of multivariate t-factor analyzers model to include constraints on the degrees of freedom, the factor loadings, and the error variance matrices. The result is a family of six mixture models, including parsimonious models. Parameter estimates for this family of models are derived using an alternating expectation-conditional maximization algorithm and convergence is determined based on Aitken's acceleration. Model selection is carried out using the Bayesian information criterion (BIC) and the integrated completed likelihood (ICL). This novel family of mixture models is then applied to simulated and real data where clustering performance meets or exceeds that of established model-based clustering methods. The simulation studies include a comparison of the BIC and the ICL as model selection techniques for this novel family of models. Application to simulated data with larger dimensionality is also explored.
机译：基于模型的聚类通常涉及混合模型家族的开发以及将这些模型施加到数据上。然后使用某些准则选择家庭中的最佳成员，并且相关的参数估计会导致预测的组成员身份或聚类。本文描述了多元t因子分析器模型的混合的扩展，以包括对自由度，因子负载和误差方差矩阵的约束。结果是六个混合模型的族，包括简约模型。使用交替期望条件最大化算法得出该系列模型的参数估计值，并根据Aitken的加速度确定收敛性。使用贝叶斯信息准则（BIC）和集成完成似然度（ICL）进行模型选择。然后，将这种新颖的混合模型系列应用于聚类性能达到或超过已建立的基于模型的聚类方法的模拟和真实数据。仿真研究包括比较BIC和ICL作为该新型模型家族的模型选择技术。还探讨了将其应用于较大维度的模拟数据。

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