High dimensional Model Based Clustering with non-Gaussian Distributions

点击翻译按钮获取中文摘要

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. *****