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Modelling the role of variables in model-based cluster analysis

机译：建模变量在基于模型的聚类分析中的作用

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摘要

In the framework of cluster analysis based on Gaussian mixture models, it is usually assumed that all the variables provide information about the clustering of the sample units. Several variable selection procedures are available in order to detect the structure of interest for the clustering when this structure is contained in a variable sub-vector. Currently, in these procedures a variable is assumed to play one of (up to) three roles: (1) informative, (2) uninformative and correlated with some informative variables, (3) uninformative and uncorrelated with any informative variable. A more general approach for modelling the role of a variable is proposed by taking into account the possibility that the variable vector provides information about more than one structure of interest for the clustering. This approach is developed by assuming that such information is given by non-overlapped and possibly correlated sub-vectors of variables; it is also assumed that the model for the variable vector is equal to a product of conditionally independent Gaussian mixture models (one for each variable sub-vector). Details about model identifiability, parameter estimation and model selection are provided. The usefulness and effectiveness of the described methodology are illustrated using simulated and real datasets.
机译：在基于高斯混合模型的聚类分析框架中，通常假定所有变量都提供有关样本单位聚类的信息。有几种变量选择过程可供使用，以便在该结构包含在变量子向量中时为聚类检测感兴趣的结构。当前，在这些过程中，假定变量扮演（最多）三个角色之一：（1）信息性；（2）无信息性且与某些信息性变量相关；（3）无信息性且与任何信息性变量不相关。通过考虑变量向量为聚类提供有关一个以上感兴趣结构的信息的可能性，提出了一种对变量的角色进行建模的更通用的方法。通过假设这种信息是由变量的非重叠且可能相关的子向量给出的，从而开发出这种方法。还假设变量向量的模型等于条件独立的高斯混合模型的乘积（每个变量子向量一个）。提供了有关模型可识别性，参数估计和模型选择的详细信息。使用模拟和真实数据集说明了所描述方法的有用性和有效性。

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