# Learning Graph Filters for Structure-Function Coupling based Hub Node Identification

arXiv: https://arxiv.org/abs/2410.17410 · HTML: https://mlsanity.com/paper/2410.17410/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 102 references that are in the map.
- First posted on arXiv 22 Oct 2024.

## Builds on (most cited first, 23 of 23)

- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [Interpreting and Unifying Graph Neural Networks with An Optimization Framework](https://mlsanity.com/paper/2101.11859/) (2021)
- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Graph signal processing for machine learning: A review and new perspectives](https://mlsanity.com/paper/2007.16061/) (2020)
- [Network Topology Inference from Spectral Templates](https://mlsanity.com/paper/1608.03008/) (2016)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [A User Guide to Low-Pass Graph Signal Processing and its Applications](https://mlsanity.com/paper/2008.01305/) (2020)
- [Sampling of graph signals with successive local aggregations](https://mlsanity.com/paper/1504.04687/) (2015)
- [Graph Learning from Filtered Signals: Graph System and Diffusion Kernel Identification](https://mlsanity.com/paper/1803.02553/) (2018)
- [Small-World Brain Networks Revisited](https://mlsanity.com/paper/1608.05665/) (2016)
- [MADMM: a generic algorithm for non-smooth optimization on manifolds](https://mlsanity.com/paper/1505.07676/) (2015)
- [Detection of false data injection attacks in smart grids based on graph signal processing](https://mlsanity.com/paper/1810.04894/) (2018)
- [Decoupling of brain function from structure reveals regional behavioral specialization in humans](https://mlsanity.com/paper/1905.07813/) (2019)
- [Bayesian Estimation of Graph Signals](https://mlsanity.com/paper/2103.15520/) (2021)
- [Filter Design for Autoregressive Moving Average Graph Filters](https://mlsanity.com/paper/1711.09086/) (2017)
- [Evaluating Graph Signal Processing for Neuroimaging Through Classification and Dimensionality Reduction](https://mlsanity.com/paper/1703.01842/) (2017)
- [Blind Inference of Eigenvector Centrality Rankings](https://mlsanity.com/paper/2008.11330/) (2020)
- [Graph-signal Reconstruction and Blind Deconvolution for Structured Inputs](https://mlsanity.com/paper/2105.14747/) (2021)
- [Community-based anomaly detection using spectral graph filtering](https://mlsanity.com/paper/2201.09936/) (2022)
- [Locating Temporal Functional Dynamics of Visual Short-Term Memory Binding using Graph Modular Dirichlet Energy](https://mlsanity.com/paper/1606.02587/) (2016)
- [Spectral Characterization of functional MRI data on voxel-resolution cortical graphs](https://mlsanity.com/paper/1910.09507/) (2019)
- [Estimating Centrality Blindly from Low-pass Filtered Graph Signals](https://mlsanity.com/paper/1910.13137/) (2019)
- [Functional Alignment with Anatomical Networks is Associated with Cognitive Flexibility](https://mlsanity.com/paper/1611.08751/) (2016)

## Built on by (most cited first, 1 of 1)

- [Co-Hub Node Based Multiview Graph Learning with Theoretical Guarantees](https://mlsanity.com/paper/2512.12435/) (2025)

## Abstract (arXiv)

Over the past two decades, tools from network science have been leveraged to characterize the organization of both structural and functional networks of the brain. One such measure of network organization is hub node identification. Hubs are specialized nodes within a network that link distinct brain units corresponding to specialized functional processes. Conventional methods for identifying hub nodes utilize different types of centrality measures and participation coefficient to profile various aspects of nodal importance. These methods solely rely on the functional connectivity networks constructed from functional magnetic resonance imaging (fMRI), ignoring the structure-function coupling in the brain. In this paper, we introduce a graph signal processing (GSP) based hub detection framework that utilizes both the structural connectivity and the functional activation to identify hub nodes. The proposed framework models functional activity as graph signals on the structural connectivity. Hub nodes are then detected based on the premise that hub nodes are sparse, have higher level of activity compared to their neighbors, and the non-hub nodes' activity can be modeled as the output of a graph-based filter. Based on these assumptions, an optimization framework, GraFHub, is formulated to learn the coefficients of the optimal polynomial graph filter and detect the hub nodes. The proposed framework is evaluated on both simulated data and resting state fMRI (rs-fMRI) data from Human Connectome Project (HCP).