CIF: SMALL: Circles of Trust: An Axiomatic Construction of Clustering in Asymmetric Networks

这个计画发展了一个不对称网路的阶层群聚的公理化理论，这是典型的信任传播。例如，假设米兰达信任比利，比利信任阿里尔，阿里尔信任米兰达，但是在相反的方向上没有足够的互动来建立信任。当这三个人相遇时，他们会互相信任吗？这个问题的答案相当于确定米兰达、比利和阿里尔是否属于同一个集群：他们的信任圈。价值、影响和转化的公理被假定。价值公理说，在一个双节点网络中，节点的聚类分辨率等于它们之间的最大相异性。影响公理说，在不允许形成双向路径的分辨率下不会形成集群。转换公理指出，如果我们考虑一个网络并减少所有成对的不相似性，那么两个节点成为同一集群的一部分的级别不会大于它们在原始网络中聚集在一起的级别。任何方法，满足这些公理的通用属性进行了探讨，并得出遵守这些公理的具体方法。为了丰富非对称聚类的公理化探索，本文提出了一个应用方向和三个理论方向。应用主旨探讨了信任圈的形成在社交网络和协议的设计，以建立信任的技术网络。理论的重点将研究替代公理公式，非对称层次聚类算法的稳定性，并确定算法来计算层次clusters.The教育议程是整合到市场和社会系统工程（MKSE）在宾夕法尼亚大学的程序。MKSE计划是一门本科课程，完全整合了设计和分析正在重塑我们社会的复杂网络所需的学科。考虑到信任在这些网络中的重要性，在该项目的背景下进行的研究被纳入MKSE计划的课程中。像信任传播的形式化这样的想法所产生的兴奋被进一步利用，以引起更广泛学术界对MKSE和系统工程项目的关注。这些想法是PI长期努力的一部分，有助于缩小兴奋，挑战和纪律差距。

This project develops an axiomatic theory of hierarchical clustering for asymmetric networks as is typical of trust propagation. Say, for example, that Miranda trusts Billy who trusts Ariel who trusts Miranda, but there has not been enough interactions in the opposite direction to establish trust. When these three people meet, shall they trust each other? The answer to this question is equivalent to the determination of whether Miranda, Billy, and Ariel are part of the same cluster: their circle of trust. The axioms of value, influence, and transformation are postulated. The Axiom of Value says that in a two-node network the nodes cluster at resolution equal to the maximum dissimilarity between them. The Axiom of Influence says that no clusters are formed at resolutions that do not allow bidirectional paths to be formed. The Axiom of Transformation states that if we consider a network and reduce all pairwise dissimilarities, the level at which two nodes become part of the same cluster is not larger than the level at which they were clustered together in the original network. Generic properties of any method that satisfies these axioms are explored and specific methods that abide by these axioms are derived. To enrich the axiomatic exploration of asymmetric clustering an application thrust and three theory thrusts are pursued. The application thrust explores the formation of circles of trust in social networks and the design of protocols to establish trust in technological networks. The theory thrusts will study alternative axiomatic formulations, stability of asymmetric hierarchical clustering algorithms, and the determination of algorithms to compute hierarchical clusters.The educational agenda is integrated into the Market and Social Systems Engineering (MKSE) program at the University of Pennsylvania. The MKSE program is an undergraduate course of study that fully integrates the disciplines needed to design and analyze the complex networks that are reshaping our society. Given the importance of trust in these networks the research undertaken in the context of this project is incorporated into classes in the MKSE program. The excitement an idea like the formalization of trust propagation generates is further exploited to draw attention to the MKSE and Systems Engineering programs from the wider academic community. These ideas are part of a long term effort on the part of the PI to contribute to the closing of the excitement, challenge, and discipline gaps.