Mixtures of Contaminated Shifted Asymmetric Laplace Factor Analyzers

聚类分析可以被定义为在数据中搜索感兴趣的组。当有限混合模型用于聚类分析时，称为基于模型的聚类。通常，新的基于模型的聚类方法的发展集中在高斯混合模型上。不幸的是，假设观测数据的子总体是高斯分布的往往是不现实的。本文提出的研究将通过开发非高斯分布的有限混合来扩展当前关于基于模型的聚类的文献。具体地说，将开发一种受污染的移位不对称拉普拉斯因子分析仪(MCSALFA)的混合物。该模型将非常适合于分析包含虚假、离奇或噪声观测的高维和大数据。特别令人感兴趣的是变量数量超过观察数量的数据集，例如来自微阵列基因表达分析的数据集。

Cluster analysis can be defined as the search for interesting groups within data. When a finite mixture model is used for cluster analysis, it is called model-based clustering. Typically, the development of novel model-based clustering approaches has focused on the Gaussian mixture model. Unfortunately, the assumption that the subpopulations of the observed data are Gaussian distributed is ofttimes unrealistic. The research proposed herein will extend the current literature on model-based clustering via development of finite mixtures of non-Gaussian distributions. Specifically, a mixture of contaminated shifted asymmetric Laplace factor analyzers (MCSALFA) will be developed. This model will be well suited for the analysis of high-dimensional and big data that contain spurious, outlying, or noisy observations. Of special interest are data sets whose number of variables exceeds the number of observations, like those arising from microarray gene expression analysis.