基于高阶网络离散外微积分的复杂网络评分与排名推断分析
Analysis of the inference of ratings and rankings in complex networks using discrete exterior calculus on higher--order networks
AI总结：
本文基于离散外微积分研究复杂网络中的排名推断，系统分析HodgeRank方法在淬致无序和四种网络模型下的性能，发现排名检索随无序强度从完美向非完美转变，推进了相关理论认知。
摘要：
排名推断是社会选择理论的核心研究内容，该理论旨在从成对比较等集体生成数据中确立偏好关系，应用场景涵盖政治选举、基于赛事结果的运动员排名、利用超链接网络的搜索引擎网页排序，以及基于用户行为的网店推荐生成等。目前已有多种从不完整或冲突数据中推断排名的方法，其中Jiang等人[Math. Program. 127, 203 (2011)]提出的HodgeRank（霍奇排名）方法，利用高阶网络中上同调链的霍奇分解，分离影响评分的梯度分量与循环分量，可实现项目列表评分与排名的简约推断。本文系统研究了HodgeRank在淬致无序影响下，以及由四种不同网络模型生成的复杂拓扑网络中的性能表现。结果显示，随着淬致无序强度的增加，系统会从真实排名完美检索阶段过渡到非完美检索阶段。本文分析了一系列可观测量，并刻画了其随网络模型参数的标度行为。该工作推进了对社会选择理论及复杂网络结构中评分与排名推断的认知。
英文摘要：
The inference of rankings plays a central role in the theory of social choice, which seeks to establish preferences from collectively generated data, such as pairwise comparisons. Examples include political elections, ranking athletes based on competition results, ordering web pages in search engines using hyperlink networks, and generating recommendations in online stores based on user behavior. Various methods have been developed to infer rankings from incomplete or conflicting data. One such method, HodgeRank, introduced by Jiang {\em et al.}~[Math. Program. {\bf 127}, 203 (2011)], utilizes Hodge decomposition of cochains in higher--order networks to disentangle gradient and cyclical components contributing to rating scores, enabling a parsimonious inference of ratings and rankings for lists of items. This paper presents a systematic study of HodgeRank's performance under the influence of quenched disorder and across networks with complex topologies generated by four different network models. The results reveal a transition from a regime of perfect retrieval of true rankings to one of imperfect retrieval as the strength of the quenched disorder increases. A range of observables are analyzed, and their scaling behavior with respect to the network model parameters is characterized. This work advances the understanding of social choice theory and the inference of ratings and rankings within complex network structures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
