三元变量间一维流形依赖关系的检测

摘要

Maximal information coefficient (MIC) is a good measure for detecting linear and nonlinear correlation between pairs of variables,but not directly applicable for triplets.Based on the idea of MIC and concept of total correlation, we propose the maximal total correlation coefficient (MTCC),which measures a one-dimensional manifold dependence a-mong three variables with a score in [0,1],where 0 stands for the weakest and 1 for the strongest.Using the strategy of computing MIC,we also present an efficient dynamic programming method to approximate the true value of MTCC in prac-tice.Simulation results show that MTCC has better generality and better equitability than nonlinear correlation information entropy ( NCIE) .By analyzing real datasets,we further verify the feasibility of MTCC.Finally,we emphasize its specificity.%最大信息系数（ Maximum Information Coefficient ，MIC）能够很好的检测成对变量间的线性和非线性依赖关系，但却不能直接用于检测三元变量间的相关关系．基于MIC的思想和全相关的概念，本文提出了一种直接检测三元变量间一维流形依赖关系的方法—最大全相关系数（Maximal Total Correlation Coefficient ，MTCC）．MTCC用落在[0，1]区间上的值来表明三元变量间一维流形依赖关系的强弱，其中0和1分别表示最弱和最强的依赖关系．使用MIC的计算策略，本文还提出了一种有效的动态规划方法来近似计算MTCC的值．仿真实验说明MTCC与非线性相关信息熵（ Nonlinear Correlation Information Entropy ，NCIE）相比具有更好的通用性和公平性，真实数据的分析验证了MTCC的实用性．最后，强调了其专用性．