产品网络的双曲结构  

The hyperbolic geometry of the product network

作　　者：张忠元[1] 齐霁 齐雯 ZHANG Zhongyuan;QI Ji;QI Wen(School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 102206, China;School of Finance, Central University of Finance and Economics, Beijing 102206, China)

机构地区：[1]中央财经大学统计与数学学院,北京102206 [2]中央财经大学金融学院,北京102206

出　　处：《辽宁师范大学学报（自然科学版）》2021年第3期301-308,共8页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(61203295);中央财经大学学科建设经费资助项目。

摘　　要：从几何学角度分析全球产品空间的复杂网络结构和升级演化过程.根据国际贸易标准分类(SITC4)构造了全球产品网络,并验证了其隐藏的度量空间是双曲几何的.采用四种网络嵌入算法,并通过Stress指标和网络重构任务的AUPR指标,验证了基于双曲几何的网络嵌入算法的结果优良性.最后通过方差分析检验了双曲嵌入结果的坐标经济学意义,其径坐标代表了产品的流行度且与其产品质量相关,其角坐标表示产品之间的相似性且在双曲空间中的分布与产品的类别划分有关.This paper analyzes the complex network structure and upgrading evolution process of the product network from the perspective of geometry.According to Standard International Trade Classification(SITC4),the global product network is constructed,and its hidden metric space is well-represented by hyperbolic geometry.Four network embedding algorithms are used and the good performance of network embedding algorithm based on hyperbolic geometry is verified by Stress and AUPR.Finally,the economical meaning of hyperbolic embedding results is tested by ANOVA analysis.Its radial coordinate represents the“popularity”of products and is significantly related to their quality.And its angular coordinate shows the“similarity”between products and its distribution in hyperbolic space is linked with the classification of products.

关 键 词：全球产品网络 双曲几何 网络嵌入 方差分析 

分 类 号：F753[经济管理—国际贸易]