MODEL-BASED GAUSSIAN AND NON-GAUSSIAN CLUSTERING
MODEL-BASED GAUSSIAN AND NON-GAUSSIAN CLUSTERING
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DOI：
10.2307/2532201
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发表时间：
1993-09-01
期刊：
影响因子：
1.9
通讯作者：
RAFTERY, AE
中科院分区：
文献类型：
--
作者：
BANFIELD, JD;RAFTERY, AE
分类最大似然方法足够普遍，以包含许多当前的聚类算法，包括基于平方和准则和Friedman和Rubin（1967，Journal of the American Statistical Association 62，1159 -1178）的准则的聚类算法。然而，如目前所实现的，它不允许指定哪些特征（方向、大小和形状）对于所有集群是共同的，以及哪些特征在集群之间可能不同。此外，它仅限于高斯分布，它不允许噪声。我们提出了克服这些限制的方法。协方差矩阵的重新参数化允许我们指定所有聚类的一些（但不是全部）特征是相同的。概述了非高斯聚类的实用框架，并描述了以泊松过程形式引入噪声的方法。给出了一种近似贝叶斯聚类数选择方法，并通过仿真研究了该方法的性能，得到了令人鼓舞的结果。将该方法应用于糖尿病研究中出现的数据集的分析，结果似乎优于以前的分析。还分析了大脑的磁共振图像（MRI），并且该方法在提取解剖学感兴趣的主要特征方面似乎是成功的。这里描述的方法已经在Fortran和S-PLUS版本中实现，该软件可以通过StatLib免费获得。
The classification maximum likelihood approach is sufficiently general to encompass many current clustering algorithms, including those based on the sum of squares criterion and on the criterion of Friedman and Rubin (1967, Journal of the American Statistical Association 62,1159-1178). However, as currently implemented, it does not allow the specification of which features (orientation, size, and shape) are to be common to all clusters and which may differ between clusters. Also, it is restricted to Gaussian distributions and it does not allow for noise.We propose ways of overcoming these limitations. A reparameterization of the covariance matrix allows us to specify that some, but not all, features be the same for all clusters. A practical framework for non-Gaussian clustering is outlined, and a means of incorporating noise in the form of a Poisson process is described. An approximate Bayesian method for choosing the number of clusters is given.The performance of the proposed methods is studied by simulation, with encouraging results. The methods are applied to the analysis of a data set arising in the study of diabetes, and the results seem better than those of previous analyses. A magnetic resonance image (MRI) of the brain is also analyzed, and the methods appear successful in extracting the main features of anatomical interest. The methods described here have been implemented in both Fortran and S-PLUS versions, and the software is freely available through StatLib.