论文标题

经常分段符合时间网络中的块模型

Recurrent segmentation meets block models in temporal networks

论文作者

Arachchi, Chamalee Wickrama, Tatti, Nikolaj

论文摘要

模型交互的一种流行方法是将它们表示为一个网络,其中节点是代理,而交互为边缘。相互作用通常是时间戳,这会导致时间戳边缘。许多现实世界中的时间网络具有反复或可能的循环行为。例如,在一天中的某些小时内,社交网络活动可能会增加。在本文中,我们的主要兴趣是在此类时间网络中对复发活动进行建模。作为起点,我们使用随机块模型,这是建模静态网络的流行选择,其中节点分为$ r $组。我们通过使用泊松过程对边缘进行建模,将此模型扩展到时间网络。我们通过将时间行分割为$ k $段来使过程的参数取决于时间。为了强制执行重复的活动,我们要求只能使用$ h <k $不同的参数集,也就是说,几个,不一定是连续的,必须共享其参数。我们证明,寻找最佳块和分割是NP困难的问题。因此,我们将问题分为3个子问题,在该子问题中,我们依次优化块,模型参数和分割,同时保持剩余结构固定。我们提出了一种迭代算法,该算法需要$ o(khm + rn + r^2h)$每迭代,其中$ n $和$ m $是网络中的节点和边缘的数量。我们通过实验证明,所需迭代的数量通常很少,算法能够从合成数据集中发现地面真相,并证明某些现实世界网络表现出复发行为,因为当$ H $降低$ H $时,可能性不会恶化。

A popular approach to model interactions is to represent them as a network with nodes being the agents and the interactions being the edges. Interactions are often timestamped, which leads to having timestamped edges. Many real-world temporal networks have a recurrent or possibly cyclic behaviour. For example, social network activity may be heightened during certain hours of day. In this paper, our main interest is to model recurrent activity in such temporal networks. As a starting point we use stochastic block model, a popular choice for modelling static networks, where nodes are split into $R$ groups. We extend this model to temporal networks by modelling the edges with a Poisson process. We make the parameters of the process dependent on time by segmenting the time line into $K$ segments. To enforce the recurring activity we require that only $H < K$ different set of parameters can be used, that is, several, not necessarily consecutive, segments must share their parameters. We prove that the searching for optimal blocks and segmentation is an NP-hard problem. Consequently, we split the problem into 3 subproblems where we optimize blocks, model parameters, and segmentation in turn while keeping the remaining structures fixed. We propose an iterative algorithm that requires $O(KHm + Rn + R^2H)$ time per iteration, where $n$ and $m$ are the number of nodes and edges in the network. We demonstrate experimentally that the number of required iterations is typically low, the algorithm is able to discover the ground truth from synthetic datasets, and show that certain real-world networks exhibit recurrent behaviour as the likelihood does not deteriorate when $H$ is lowered.

扫码加入交流群

加入微信交流群

微信交流群二维码

扫码加入学术交流群,获取更多资源