图上信息传播的模型
Models for information propagation on graphs
AI总结：
本文提出并统一了图上信息传播的三类模型（波前传播、广义旅行时间最小化、程函方程），证明其等价性，并应用于半监督学习和信任网络。
摘要：
我们提出并统一了图上信息传播的不同模型类别。在第一类中，传播被建模为一种波，该波在初始时刻从一组已知节点发出，在后续时刻传播到所有其他未知节点，其顺序由信息波前的到达时间决定。第二类模型基于节点间路径上的旅行时间概念。从初始已知节点集到某个节点的信息传播时间被定义为所有可容许路径子集上广义旅行时间的最小值。最后一类通过在每个未知节点处施加程函形式的局部方程，并在已知节点处施加边界条件来给出。节点处局部方程的解值与其相邻且值较低的节点的解值相耦合。我们提供了这些模型类别的精确表述，并证明了它们之间的等价性。最后，我们将图上的波前传播模型应用于通过标签传播的半监督学习以及信任网络上的信息传播。
英文摘要：
We propose and unify classes of different models for information propagation over graphs. In a first class, propagation is modelled as a wave which emanates from a set of \emph{known} nodes at an initial time, to all other \emph{unknown} nodes at later times with an ordering determined by the arrival time of the information wave front. A second class of models is based on the notion of a travel time along paths between nodes. The time of information propagation from an initial \emph{known} set of nodes to a node is defined as the minimum of a generalised travel time over subsets of all admissible paths. A final class is given by imposing a local equation of an eikonal form at each \emph{unknown} node, with boundary conditions at the \emph{known} nodes. The solution value of the local equation at a node is coupled to those of neighbouring nodes with lower values. We provide precise formulations of the model classes and prove equivalences between them. Finally we apply the front propagation models on graphs to semi-supervised learning via label propagation and information propagation on trust networks.
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。
