High dimensional Model Based Clustering with non-Gaussian Distributions

建议研究有两个主要目标：为非正态分布*(如Kotz分布)构建一个有效且一致的估计程序；以及开发一个使用基于模型的聚类的内在维建模框架。在基于模型的聚类中，假设异质数据是由有限混合模型生成的。Kotz分布被用来模拟尖峰和尖峰数据。Kotz分布包含幂指数分布和多元正态分布作为特例。我们建议研究Kotz分布和广义Kotz分布在基于模型的聚类中的性能。一个挑战是，目前还没有用于Kotz分布的参数估计程序。*在聚类中，一个本征维度能够有效地捕捉聚类内部的本质或变化，是典型的低维空间。许多基于模型的聚类方法假定存在某种形式的内在维度。补码(外部或噪声)维度包含剩余的变量，本质上是噪声。我们提出了一个本征维和噪声维的密度不同的框架。*****

The proposal research has two primary objectives; construct an efficient and consistent estimation procedure for non-normal distributions***such as the Kotz distribution, and develop a framework for Intrinsic Dimension Modelling using model-based clustering. In model-based clustering assumes the heterogeneous data was generated by a finite mixture model. The Kotz distribution has been proposed for model both leptokurtic and platykurtic data. The Kotz distribution contains the power exponential distribution and the multivariate normal as special cases. We propose to investigate the performance of the Kotz distribution and the generalized Kotz distribution in model-based clustering. One challenge is that there is no current parameter estimation procedure for the Kotz distribution. ******In clustering, an intrinsic dimension captures the essence or effectively the variation within cluster and is typically a low-dimensional space. Many model-based clustering methods assume some form of an intrinsic dimension. The complement (extrinsic or noise) dimension contains the remaining variation and is essentially noise. We propose a framework where the densities of the intrinsic and noise dimensions vary. *****