Search Results for author:
Found 18 papers, 8 papers with code
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.
Spectral Topological Data Analysis of Brain Signals
Our approach, the spectral TDA (STDA), has the ability to capture more nuanced and detailed information about the underlying brain networks.
Sulcal Pattern Matching with the Wasserstein Distance
We present the unified computational framework for modeling the sulcal patterns of human brain obtained from the magnetic resonance images.
Altered Topological Structure of the Brain White Matter in Maltreated Children through Topological Data Analysis
Childhood maltreatment may adversely affect brain development and consequently influence behavioral, emotional, and psychological patterns during adulthood.
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.
Unified Topological Inference for Brain Networks in Temporal Lobe Epilepsy Using the Wasserstein Distance
Persistent homology offers a powerful tool for extracting hidden topological signals from brain networks.
Hodge-Decomposition of Brain Networks
We analyze brain networks by decomposing them into three orthogonal components: gradient, curl, and harmonic flows, through the Hodge decomposition, a technique advantageous for capturing complex topological features.
Dynamic Topological Data Analysis of Functional Human Brain Networks
We propose a novel dynamic-TDA framework that builds persistent homology over a time series of brain networks.
Embedding of Functional Human Brain Networks on a Sphere
Human brain activity is often measured using the blood-oxygen-level dependent (BOLD) signals obtained through functional magnetic resonance imaging (fMRI).
Topological Data Analysis of Human Brain Networks Through Order Statistics
Understanding the common topological characteristics of the human brain network across a population is central to understanding brain functions.
Statistical Analysis on Brain Surfaces
In this paper, we review widely used statistical analysis frameworks for data defined along cortical and subcortical surfaces that have been developed in last two decades.
Persistent Homological State-Space Estimation of Functional Human Brain Networks at Rest
We introduce an innovative, data-driven topological data analysis (TDA) technique for estimating the state spaces of dynamically changing functional human brain networks at rest.
Hodge-Laplacian of Brain Networks
The closed loops or cycles in a brain network embeds higher order signal transmission paths, which provide fundamental insights into the functioning of the brain.
Lattice Paths for Persistent Diagrams
We then develop a new exact statistical inference procedure for lattice paths via combinatorial enumerations.
Graph Theory in Brain Networks
Recent developments in graph theoretic analysis of complex networks have led to deeper understanding of brain networks.
Topological Learning for Brain Networks
This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology.
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.
