This work presents a mixture model allowing to cluster variables of different types. All variables being measured on the same n statistical units, we first represent every variable with a unit-norm operator in \({\mathbb {R}}^{n\times n}\) endowed with an appropriate inner product. We propose a von Mises–Fisher mixture model on the unit-sphere containing these operators. The parameters of the mixture model are estimated with an EM algorithm, combined with a K-means procedure to obtain a good starting point. The method is tested on simulated data and eventually applied to wine data.

中文翻译：

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用于聚类数值和分类变量的 von Mises-Fisher 混合模型

这项工作提出了一个混合模型，允许对不同类型的变量进行聚类。所有变量都在相同的n 个统计单位上进行测量，我们首先用\({\mathbb {R}}^{n\times n}\) 中的单位范数运算符表示每个变量，并赋予适当的内积。我们在包含这些算子的单位球体上提出了一个 von Mises-Fisher 混合模型。混合模型的参数用EM算法估计，结合K-means程序以获得良好的起点。该方法在模拟数据上进行了测试，并最终应用于葡萄酒数据。