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Found 11 papers, 0 papers with code
Topological Cycle Graph Attention Network for Brain Functional Connectivity
This study, we introduce a novel Topological Cycle Graph Attention Network (CycGAT), designed to delineate a functional backbone within brain functional graph--key pathways essential for signal transmissio--from non-essential, redundant connections that form cycles around this core structure.
Advancing Graph Neural Networks with HL-HGAT: A Hodge-Laplacian and Attention Mechanism Approach for Heterogeneous Graph-Structured Data
Additionally, we propose a pooling operator to coarsen $k$-simplices, combining features through simplicial attention mechanisms of self-attention and cross-attention via transformers and SP operators, capturing topological interconnections across multiple dimensions of simplices.
Heterogeneous Graph Convolutional Neural Network via Hodge-Laplacian for Brain Functional Data
We introduce a generic formulation of spectral filters on heterogeneous graphs by introducing the $k-th$ Hodge-Laplacian (HL) operator.
Increasing Fairness via Combination with Learning Guarantees
Furthermore, we investigate the properties of the proposed measure and propose first- and second-order oracle bounds to show that fairness can be boosted via ensemble combination with theoretical learning guarantees.
Revisiting convolutional neural network on graphs with polynomial approximations of Laplace-Beltrami spectral filtering
This paper revisits spectral graph convolutional neural networks (graph-CNNs) given in Defferrard (2016) and develops the Laplace-Beltrami CNN (LB-CNN) by replacing the graph Laplacian with the LB operator.
Fast Mesh Data Augmentation via Chebyshev Polynomial of Spectral filtering
Even though graph convolutional neural network (graph-CNN) has been widely used in deep learning, there is a lack of augmentation methods to generate data on graphs or surfaces.
Fast Polynomial Approximation of Heat Kernel Convolution on Manifolds and Its Application to Brain Sulcal and Gyral Graph Pattern Analysis
We also derive the closed-form expression of the spectral decomposition of the Laplace-Beltrami operator and use it to solve heat diffusion on a manifold for the first time.
Convolutional Neural Network on Semi-Regular Triangulated Meshes and its Application to Brain Image Data
We developed a convolution neural network (CNN) on semi-regular triangulated meshes whose vertices have 6 neighbours.
Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images
Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights.
Bayesian Estimation of White Matter Atlas from High Angular Resolution Diffusion Imaging
We first assume that the atlas is generated from a known hyperatlas through a flow of diffeomorphisms and its shape prior can be constructed based on the framework of large deformation diffeomorphic metric mapping (LDDMM).
Diffeomorphic Metric Mapping and Probabilistic Atlas Generation of Hybrid Diffusion Imaging based on BFOR Signal Basis
In this work, we show that the reorientation of the $q$-space signal due to spatial transformation can be easily defined on the BFOR signal basis.
