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Model-based Clustering With Non-elliptically Contoured Distributions

机译：具有非椭圆轮廓分布的基于模型的聚类

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摘要

The majority of the existing literature on model-based clustering deals with symmetric components. In some cases, especially when dealing with skewed subpopulations, the estimate of the number of groups can be misleading; if symmetric components are assumed we need more than one component to describe an asymmetric group. Existing mixture models, based on multivariate normal distributions and multivariate t distributions, try to fit symmetric distributions, i.e. they fit symmetric clusters. In the present paper, we propose the use of finite mixtures of the normal inverse Gaussian distribution (and its multivariate extensions). Such finite mixture models start from a density that allows for skewness and fat tails, generalize the existing models, are tractable and have desirable properties. We examine both the univariate case, to gain insight, and the multivariate case, which is more useful in real applications. EM type algorithms are described for fitting the models. Real data examples are used to demonstrate the potential of the new model in comparison with existing ones.
机译：现有的有关基于模型的聚类的大多数文献都涉及对称组件。在某些情况下，尤其是在处理倾斜的子群体时，对组数的估计可能会产生误导；如果假设对称分量，则我们需要一个以上的分量来描述一个不对称的组。基于多元正态分布和多元t分布的现有混合模型试图拟合对称分布，即它们适合对称簇。在本文中，我们建议使用正态高斯逆分布（及其多元扩展）的有限混合。这样的有限混合模型从允许偏斜和肥尾的密度开始，概括了现有模型，易于处理并具有理想的特性。我们既检查单变量情况以获取洞察力，也检查多变量情况，这在实际应用中更为有用。描述了用于拟合模型的EM类型算法。实际数据示例用于证明新模型与现有模型相比的潜力。

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