高维分类数据的关联关系及可压缩性分析

Analysis of correlation and compressibility of high-dimensional categorical data

对于高维情形而言,研究变量之间的关联关系及可压缩性是重要和繁琐的.首先,给出了基于对数线性模型和关联图的压缩性定理;然后,讨论了基于条件互信息可压缩性排序的问题,并通过三个不同的实例进行验证分析.研究结果为直观简便地分析高维分类数据的关系及结构提供了方法.

For high-dimensional categorical data,the study of the correlation and the compressibility among variables is significant and complicated.In the present study,the theorem of compressibility based on the log-linear model and the corre-lation diagram is provided,and the issue of the sequencing compressibility based on the conditional mutual information is discussed.In addition,the verification analysis is carried out through three different examples,and we find that the com-pressible variables are in a relatively compressible position in the compressible sort.The research findings providing methods to intuitively and succinctly analyze the relation and the structure of high-dimensional categorical data.