基于主成分分析的网络节点重要性指标贡献评价

Contribution Analysis for Assessing Node Importance Indices with Principal Component Analysis

为研究不同网络节点重要性指标对网络中重要节点的影响程度,进而优选出较能体现网络重要节点性质的指标.本文基于主成分分析(Principal Component Analysis,简记PCA),选取七个节点重要性指标对网络重要性节点贡献率进行计算分析,同时选取了七种不同的网络进行实验,得到指标贡献率大小顺序,利用肯德尔系数对重要指标与其余指标进行相关性分析,得到不同指标之间的相关系数及相关系数大小的影响因素.本文为研究网络重要节点选择指标提供了一种思路,同时为研究不同节点间的相互关系提供了研究方法.

In network theory,it is interest to study the influences of different nodes on the key nodes in the network,and build or select the proper node importance index to model it.This paper selects seven node importance indices to calculate and analyze their contributions in nodes’ importance evaluation with Principal Component Analysis.Seven empirical networks are used for experiments.Moreover,the order of different contributions of indices is obtained,and the correlation analysis between the most important index and the other indices is carried out using the Kendall coefficient,and factors affecting the correlation coefficient are also discussed.This paper provides a way to select the node importance index in the network,and the results could also be used for studying the relationships between different nodes.