Flexible mixture modeling via the multivariate t distribution with the Box-Cox transformation: an alternative to the skew-t distribution.
Flexible mixture modeling via the multivariate t distribution with the Box-Cox transformation: an alternative to the skew-t distribution.
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DOI：
10.1007/s11222-010-9204-1
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发表时间：
2012-01-01
影响因子：
2.2
通讯作者：
Gottardo R
中科院分区：
文献类型：
--
作者：
Lo K;Gottardo R
聚类分析是对数据集中同类观察组的自动搜索。一种流行的聚类建模方法是基于有限正态混合模型，该模型假设每个聚类都被建模为多变量正态分布。然而，假设每个分量都是对称的正态分布往往是不现实的。此外，正态混合模型对异常值的健壮性不强；它们通常需要额外的组件来模拟异常值和/或给出较差的数据表示。为了解决这些问题，我们提出了一类新的分布--带Box-Cox变换的多元t分布，用于混合建模。这类分布用更重尾的t分布推广了正态分布，并通过Box-Cox变换引入了偏度。因此，这提供了一个统一的框架来同时处理离群值识别和数据转换这两个相互关联的问题。我们描述了一种用于参数估计和变换选择的期望最大化算法。我们用三个真实数据集和仿真研究对所提出的方法进行了验证。与包括Skew-t混合模型在内的多种方法相比，本文提出的带有Box-Cox变换的t混合模型在分配观测值的准确性、对模型错误指定的稳健性以及组件数目的选择等方面都表现出了良好的性能。
Cluster analysis is the automated search for groups of homogeneous observations in a data set. A popular modeling approach for clustering is based on finite normal mixture models, which assume that each cluster is modeled as a multivariate normal distribution. However, the normality assumption that each component is symmetric is often unrealistic. Furthermore, normal mixture models are not robust against outliers; they often require extra components for modeling outliers and/or give a poor representation of the data. To address these issues, we propose a new class of distributions, multivariate t distributions with the Box-Cox transformation, for mixture modeling. This class of distributions generalizes the normal distribution with the more heavy-tailed t distribution, and introduces skewness via the Box-Cox transformation. As a result, this provides a unified framework to simultaneously handle outlier identification and data transformation, two interrelated issues. We describe an Expectation-Maximization algorithm for parameter estimation along with transformation selection. We demonstrate the proposed methodology with three real data sets and simulation studies. Compared with a wealth of approaches including the skew-t mixture model, the proposed t mixture model with the Box-Cox transformation performs favorably in terms of accuracy in the assignment of observations, robustness against model misspecification, and selection of the number of components.
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影响因子：
12.3
作者：
Gentleman RC;Carey VJ;Bates DM;Bolstad B;Dettling M;Dudoit S;Ellis B;Gautier L;Ge Y;Gentry J;Hornik K;Hothorn T;Huber W;Iacus S;Irizarry R;Leisch F;Li C;Maechler M;Rossini AJ;Sawitzki G;Smith C;Smyth G;Tierney L;Yang JY;Zhang J
通讯作者：
Zhang J
影响因子：
3.7
作者：
BICKEL, PJ;DOKSUM, KA
通讯作者：
DOKSUM, KA
影响因子：
8
作者：
CELEUX, G;GOVAERT, G
通讯作者：
GOVAERT, G
DOI：
10.1111/1467-9868.00391
发表时间：
2003-01-01
影响因子：
5.8
作者：
Azzalini, A;Capitanio, A
通讯作者：
Capitanio, A
影响因子：
2.2
作者：
Andrews, Jeffrey L.;McNicholas, Paul D.
通讯作者：
McNicholas, Paul D.