一种探测多变量数据集中非线性相关性的新方法  

A Novel Approach to Evaluate Nonlinear Correlation of a Multivariable Data Set

作　　者：顾涵章 张建秋[1] 

机构地区：[1]复旦大学电子工程系,上海200433

出　　处：《复旦学报（自然科学版）》2015年第6期688-695,705,共9页Journal of Fudan University：Natural Science

基　　金：国家自然科学基金(61171127)

摘　　要：为使最大信息系数(MIC)适用于多变量数据集,给出了一种方法,该方法首先将数据集中的多个变量合并为两个变量,并且穷尽所有的合并方式.然后使用MIC来评估降维后的双变量数据集的非线性相关性.最后将所有可能的合并方式下产生的MIC值的最大值作为最终结果.由此,即得到了一种评估多变量数据集中非线性相关关系强度的新方法.理论分析表明,该方法能够有效反映原始数据集中非线性相关性强度.此外,相较于非线性相关信息熵(NCIE),该方法能够给出更明确的结果,从而是一种更优异的非线性相关性测度.In this paper, to make the maximum information coefficient （MIC） feasible to a multivariable data set, a method used to merge the multiple variables in the data set into two with all possible merging patterns is first given. The nonlinear correlation of the reduced two-variable data set is then evaluated by the MIC, where the maximum MIC value of the all possible merging patterns is taken as the final result. In this way, a novel approach to evaluate nonlinear correlation relationships in a multivariable data set is proposed. Theoretical analyses show that our approach can reflect the strength of nonlinear correlation in the original multivariable data set effectively. Compared to the nonlinear correlation information entropy （NCIE）, our approach gives more explicit results. Hence, it is a better measure of nonlinear dependence.

关 键 词：非线性相关 互信息 最大信息系数 非线性相关信息熵 

分 类 号：TN911.72[电子电信—通信与信息系统]