贝叶斯“中心聚类”：应用于西高止山脉景观分类
On Bayesian "central clustering": Application to landscape classification of Western Ghats
摘要：
对印度西海岸著名的生物多样性热点西高止山脉进行景观分类是世界范围生物多样性监测计划的重要组成部分。为此，一个庞大的植被数据集，由51,834个4变量观测组成，已被Numbra和Gadgil聚类到不同的景观中[Current Sci. 75（1998）264- 271]。但由于聚类分析的非唯一性和缺乏对聚类结果的不确定性进行量化的方法，影响了这种重要性的研究。出于这一应用问题的科学意义，我们提出了一种新的方法来获得全球，以及局部模式的聚类的后验分布，随着所需的可信和“最高后验密度”地区的非参数贝叶斯框架。为了满足计算任意两个聚类之间的距离的适当度量的需要，我们采用并提供了一个更简单的，但准确的修改的度量中提出的[在Felicitation卷在荣誉教授B。K. Kale（2009）MacMillan]。一种非常快速和有效的贝叶斯方法，基于[Sankhybrid Ser.B70（2008）133- 155]，已经被用来解决与大量数据相关联的计算问题，并从聚类的后验分布中获得样本，在此基础上说明了我们提出的概括方法。
英文摘要：
Landscape classification of the well-known biodiversity hotspot, Western Ghats (mountains), on the west coast of India, is an important part of a world-wide program of monitoring biodiversity. To this end, a massive vegetation data set, consisting of 51,834 4-variate observations has been clustered into different landscapes by Nagendra and Gadgil [Current Sci. 75 (1998) 264--271]. But a study of such importance may be affected by nonuniqueness of cluster analysis and the lack of methods for quantifying uncertainty of the clusterings obtained. Motivated by this applied problem of much scientific importance, we propose a new methodology for obtaining the global, as well as the local modes of the posterior distribution of clustering, along with the desired credible and "highest posterior density" regions in a nonparametric Bayesian framework. To meet the need of an appropriate metric for computing the distance between any two clusterings, we adopt and provide a much simpler, but accurate modification of the metric proposed in [In Felicitation Volume in Honour of Prof. B. K. Kale (2009) MacMillan]. A very fast and efficient Bayesian methodology, based on [Sankhyā Ser. B 70 (2008) 133--155], has been utilized to solve the computational problems associated with the massive data and to obtain samples from the posterior distribution of clustering on which our proposed methods of summarization are illustrated.
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