# Graph Frequency Analysis of Brain Signals

arXiv: https://arxiv.org/abs/1512.00037 · HTML: https://mlsanity.com/paper/1512.00037/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2015.

## Built on by (most cited first, 8 of 8)

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Simplified Graph Convolution with Heterophily](https://mlsanity.com/paper/2202.04139/) (2022)
- [Graph Normalized-LMP Algorithm for Signal Estimation Under Impulsive Noise](https://mlsanity.com/paper/2203.00320/) (2022)
- [Stability of Flow Models for Graph Signals](https://mlsanity.com/paper/2607.07510/) (2026)
- [Graph Contrastive Learning for Connectome Classification](https://mlsanity.com/paper/2502.05109/) (2025)
- [Reconstruction of Graph Signals on Complex Manifolds with Kernel Methods](https://mlsanity.com/paper/2505.15202/) (2025)
- [Data-Efficient Psychiatric Disorder Detection via Self-supervised Learning on Frequency-enhanced Brain Networks](https://mlsanity.com/paper/2509.10524/) (2025)
- [Learning Superpixel Ensemble and Hierarchy Graphs for Melanoma Detection](https://mlsanity.com/paper/2604.03710/) (2026)

## Abstract (arXiv)

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 task familiarity.