Cluster Analysis, Predictive Distributions, and Stochastic Search Algorithms

聚类分析是一种广泛使用的探索性工具，用于发现数据中的模式。聚类分析的基本目标是将m个可区分的对象（基于与它们相关联的测量）分成组或聚类，使得每个组内的对象是“相似的”，而组本身是“不同的”。“m个对象的可能分区的数量随着m的增长而增长得非常快，因此不可能对最佳分区进行穷举搜索。 大多数标准方法，如分层和K均值聚类：（a）为了实现速度而牺牲对所有可能分区的广泛搜索;（B）无法（全局）优化目标函数;并且通常返回单个答案，即使可能存在许多与应用程序相关的同样好的答案。 这项调查将着眼于：（一）聚类算法使用数据平滑的性能可达到的改进;（二）一个基于模型的方法，同时平滑的数据，同时提供一个自然的目标函数的排名分区;和（iii）进行随机搜索的策略与高速计算和马尔可夫链蒙特卡罗算法。所提出的方法已经成功地应用在一些例子中。聚类分析最近重新引起了人们的兴趣，部分原因是它在生物信息学中的应用，在生物信息学中，它可以与微阵列分析一起用于识别与某些疾病相关的基因组。 例如，某些基因的存在或缺乏可能使人易患某些类型的癌症，或表明某些手术的术后风险更大。 因此，拟议项目对社会的好处包括更好地理解这些关系，这些改进的算法将产生的进步，以及基因和疾病之间联系的更清晰的画面。 研究生也将接受培训，以进一步发展这些方法。 其他研究人员，在这些新方法的培训，将发现自己的调查增强。

Cluster analysis is a widely used exploratory tool for finding patterns in data. The basic goal of a cluster analysis is to separate m distinguishable objects (based on measurements associated with them) into groups, or clusters, such that the objects within each group are "similar" while the groups themselves are "different." The number of possible partitions of m objects grows extremely quickly with m, and consequently it is impossible to perform an exhaustive search for the best partition. Most standard methods such as hierarchical and K-means clustering: (a) sacrifice an extensive search of all possible partitions for speed of implementation; (b) fail to (globally) optimize an objective function; and generally return a single answer, even though there may be many equally good answers that are all relevant to the application. This investigation will look at: (i) The improvement attainable in the performance of clustering algorithms using data smoothing; (ii) A model-based approach to simultaneously smooth the data while providing a natural objective function for ranking partitions; and (iii) Strategies for conducting a stochastic search with high speed computing and Markov chain Monte Carlo algorithms. The proposed methodology has already been successfully applied in some examples.Cluster analysis has seen renewed interest of late due, in part, due to its applications in bioinformatics, where it can be used with microarray analysis to identify groups of genes that can be linked to certain diseases. For example, it could be the case that the presence or absence of certain genes could predispose a person to certain types of cancers, or to indicate greater post-operative risk from certain procedures. Therefore, the benefits to society of the proposed project include the advances from the better understanding of these relationships that these improved algorithms will yield, and the clearer picture provided of the links between genes and diseases. Graduate students will also be trained to develop these methods further. Other researchers, trained in these new methods, will find their own investigations enhanced.