Estimation and model selection for model-based clustering with the conditional classification likelihood
Estimation and model selection for model-based clustering with the conditional classification likelihood
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DOI：
10.1214/15-ejs1026
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发表时间：
2015-01-01
影响因子：
1.1
通讯作者：
Baudry, Jean-Patrick
中科院分区：
文献类型：
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作者：
Baudry, Jean-Patrick
Biernacki、Celeux和Govaert（2000年）在基于模型的聚类框架中引入了综合完成的Likestive（ICL）标准，以选择相关数量的类，并已被统计学家用于各种应用领域。对ICL进行了理论研究，给出了与聚类目标相关的对比：条件分类似然、估计量和模型选择准则。这些新的程序的性质进行了研究和ICL被证明是这些标准之一的近似。我们将这些结果与目前关于ICL的主要观点进行了对比，认为这是不一致的。此外，这些结果给出了ICL的基本类概念的见解和饲料的类概念在clustering.一般结果的惩罚最小对比度准则和上界的包围熵参数的情况下，这可能是有用的本身，提出了实用的解决方案的计算所介绍的程序，特别是自适应EM算法和用于类似EN4的算法的新的初始化方法，其有助于改进高斯混合模型中的估计。
The Integrated Completed Likelihood (ICL) criterion was introduced by Biernacki, Celeux and Govaert (2000) in the model-based clustering framework to select a relevant number of classes and has been used by statisticians in various application areas. A theoretical study of ICL is proposed.A contrast related to the clustering objective is introduced: the conditional classification likelihood, An estimator and model selection criteria are deduced. The properties of these new procedures are studied and ICL is proved to be an approximation of one of these criteria. We contrast these results with the current leading point of view about ICL, that it would not be consistent. Moreover these results give insights into the class notion underlying ICL and feed a reflection on the class notion in clustering.General results on penalized minimum contrast criteria and upper-bounds of the bracketing entropy in parametric situations are derived, which can be useful per se.Practical solutions for the computation of the introduced procedures are proposed, notably an adapted EM algorithm and a new initialization method for EN4-like algorithms which helps to improve the estimation in Gaussian mixture models.