高维纵向数据动态聚类分析研究

本项目基于增长曲线模型和马尔可夫链蒙特卡洛（MCMC）方法研究高维纵向数据动态聚类分析。实际背景来自于：高维数据聚类面临“维数灾难”（curse of dimensionality）的困难，即变量维数太大使得待估参数太多，导致无法进行有效估计和聚类分析。和截面数据相比，纵向数据具有相关性和非平衡性这两个特性，因此传统的系统聚类方法和一般的基于模型的聚类方法难于有效处理高维纵向数据聚类分析。引入增长曲线模型可以把复杂的高维数据聚类问题简化为对分类参数的估计问题，避免了高维数据“维数灾难”问题；在全空间中寻找最优聚类结果，把静态聚类拓展到动态聚类，采用MCMC方法降低动态聚类的计算量，大大提高了高维纵向数据聚类的效率。

A dynamic clustering analysis method is proposed for high-dimensional longitudinal data based on growth curve model and Markov chain Monte Carlo (MCMC) sampling. The actual background comes from the well-known "curse of dimensionality" for high-dimensional data, which is mainly due to the fact that model-based clustering methods are over-parameterized in high-dimensional spaces. Furthermore, in longitudinal studies, measurements taken over time on individuals are correlated and usually show a highly unbalanced structure. Traditionally clustering algorithms such as K-means and model-based methods are difficult to effectively deal with high-dimensional longitudinal data. The introduction of growth curve model can simplify the complex high-dimensional data clustering problem into the estimation problem of classification parameters, and avoid the "curse of dimensionality" problem of high-dimensional data. In order to find the optimal clustering results in the whole space, the static clustering was extended to the dynamic clustering, and the MCMC method was used to reduce the calculation of dynamic clustering, which greatly improved the efficiency of high-dimensional vertical data clustering.