Embedding and Trajectories of Temporal Networks
Embedding and Trajectories of Temporal Networks
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DOI：
10.1109/access.2023.3268030
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发表时间：
2022-08
期刊：
影响因子：
3.9
通讯作者：
Chanon Thongprayoon;L. Livi;N. Masuda
中科院分区：
文献类型：
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作者：
Chanon Thongprayoon;L. Livi;N. Masuda
时态网络数据在各个领域中越来越多地可用，并且通常表示具有复杂结构和时态演变的高度复杂的系统。由于处理这种复杂数据的困难，将粗粒度的时间网络数据转化为嵌入低维空间中的数值轨迹可能是有用的。我们将这样的过程称为时间网络嵌入，这与旨在嵌入单个节点的过程不同。时间网络嵌入是一项具有挑战性的任务，因为我们通常只能访问节点对之间的离散时间戳事件，并且通常事件以不规则的间隔发生，使得在给定时间构建网络已经是一个重要的问题。我们提出了一种方法来生成嵌入在低维空间中的时间网络的轨迹给定的时间戳事件序列作为输入。我们实现了这一目标相结合的地标多维尺度（LMDS），这是一个著名的多维尺度方法的样本外扩展，和领带衰变时间网络的框架。这种组合使我们能够获得描述时间网络演化的连续时间轨迹。然后，我们研究所提出的时间网络嵌入框架的数学特性。最后，我们展示了社会联系的经验数据的方法，以找到时间组织的接触事件和他们在一天内，并在不同的日子损失。
Temporal network data are increasingly available in various domains, and often represent highly complex systems with intricate structural and temporal evolutions. Due to the difficulty of processing such complex data, it may be useful to coarse grain temporal network data into a numeric trajectory embedded in a low-dimensional space. We refer to such a procedure as temporal network embedding, which is distinct from procedures that aim at embedding individual nodes. Temporal network embedding is a challenging task because we often have access only to discrete time-stamped events between node pairs, and, in general, the events occur with irregular intervals, making the construction of the network at a given time a nontrivial question already. We propose a method to generate trajectories of temporal networks embedded in a low-dimensional space given a sequence of time-stamped events as input. We realize this goal by combining the landmark multidimensional scaling (LMDS), which is an out-of-sample extension of the well-known multidimensional scaling method, and the framework of tie-decay temporal networks. This combination enables us to obtain a continuous-time trajectory describing the evolution of temporal networks. We then study mathematical properties of the proposed temporal network embedding framework. Finally, we showcase the method with empirical data of social contacts to find temporal organization of contact events and loss of them over a single day and across different days.