This paper presents methods to analyze functional brain networks and signals from graph spectral perspectives. The notion of frequency and filters traditionally defined for signals supported on regular domains such as discrete time and image grids has been recently generalized to irregular graph domains and defines brain graph frequencies associated with different levels of spatial smoothness across the brain regions. Brain network frequency also enables the decomposition of brain signals into pieces corresponding to smooth or rapid variations. We relate graph frequency with principal component analysis when the networks of interest denote functional connectivity. The methods are utilized to analyze brain networks and signals as subjects master a simple motor skill. We observe that brain signals corresponding to different graph frequencies exhibit different levels of adaptability throughout learning. Further, we notice a strong association between graph spectral properties of brain networks and the level of exposure to tasks performed and recognize the most contributing and important frequency signatures at different levels of task familiarity.

中文翻译：

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脑信号的图形频率分析

本文介绍了从图谱的角度分析功能性大脑网络和信号的方法。传统上为支持规则域（如离散时间和图像网格）的信号定义的频率和滤波器的概念最近已推广到不规则图域，并定义与跨大脑区域的不同空间平滑度水平相关的大脑图频率。大脑网络频率还能够将大脑信号分解成与平滑或快速变化相对应的片段。当感兴趣的网络表示功能连接时，我们将图频率与主成分分析相关联。当受试者掌握简单的运动技能时，这些方法用于分析大脑网络和信号。我们观察到，对应于不同图形频率的大脑信号在整个学习过程中表现出不同程度的适应性。此外，我们注意到大脑网络的图谱特性与所执行任务的暴露程度之间存在很强的关联，并在不同的任务熟悉程度下识别出最有贡献和最重要的频率特征。