用图形傅里叶分析法分析集体运动
Analyzing Collective Motion Using Graph Fourier Analysis
摘要：
动物群体中的集体运动，如成群的昆虫、成群的鸟和成群的鱼，是涌现行为中最引人注目的例子。在实验或计算模拟中对这些行为的经验分析主要涉及使用“群平均”度量或序参量，例如速度对准和角动量。最近，计算拓扑学的工具已被应用于分析群，以进一步理解和自动检测在空间和时间上进化的根本不同的群结构。在这里，我们展示了如何图形信号处理领域可以用来融合这两种方法，通过集体分析使用图形傅立叶谐波尊重群的拓扑结构的群属性。这个图形傅立叶分析揭示了一些常见的群集状态中的隐藏结构，并形成了集体运动的灵活分析框架的基础。
英文摘要：
Collective motion in animal groups, such as swarms of insects, flocks of birds, and schools of fish, are some of the most visually striking examples of emergent behavior. Empirical analysis of these behaviors in experiment or computational simulation primarily involves the use of "swarm-averaged" metrics or order parameters such as velocity alignment and angular momentum. Recently, tools from computational topology have been applied to the analysis of swarms to further understand and automate the detection of fundamentally different swarm structures evolving in space and time. Here, we show how the field of graph signal processing can be used to fuse these two approaches by collectively analyzing swarm properties using graph Fourier harmonics that respect the topological structure of the swarm. This graph Fourier analysis reveals hidden structure in a number of common swarming states and forms the basis of a flexible analysis framework for collective motion.
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