Brain Connectome Analysis for Alzheimer’s Disease using Hodge Laplacian-based Edge Convolution
Poster No:
1377
Submission Type:
Abstract Submission
Authors:
JOONHYUK PARK1, Yechan Hwang1, Moo K Chung2, Minjeong Kim3, Guorong Wu4, Won Hwa Kim1
Institutions:
1Pohang University of Science and Technology (POSTECH), Pohang, Korea, Republic of, 2University of Wisconsin, Madison, WI, 3University of North Carolina at Greensboro, Greensboro, NC, 4University of North Carolina at Chapel Hill, Chapel Hill, NC
First Author:
Co-Author(s):
Introduction:
Advancement of graph theory has facilitated the study of the human brain as a graph, depicting anatomical regions of interest (ROIs) as nodes and white matter connectomes as edges [2]. Recent brain network analysis employs graph neural networks (GNNs) that utilize graph convolution on node signals, where the analysis is performed on the node measures and the actual connectomic features play an indirect role as a neighborhood selector. Thus, we propose to utilize Hodge-GNN that can capture the edge-wise relationship and allow the spatial graph convolution to directly employ the higher-order connectivity (i.e., connectivity between edges) of a graph as a simplicial complex via Hodge Laplacian. Our method was validated on Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset and depicted Alzheimer's Disease (AD) associated brain connectivities, which aligned with existing literatures.
This research was supported by IITP-2019-0-01906 (AI Graduate Program at POSTECH), the Korea Health Industry Development Institute (KHIDI) HU22C0168 and HU22C0171, and National Research Foundation (NRF) NRF-2022R1A2C2092336.
This research was supported by IITP-2019-0-01906 (AI Graduate Program at POSTECH), the Korea Health Industry Development Institute (KHIDI) HU22C0168 and HU22C0171, and National Research Foundation (NRF) NRF-2022R1A2C2092336.
Methods:
Dataset. The dataset consists of structural brain connectivity data obtained from Diffusion Tensor Images (DTI) within ADNI using tractography. Each sample is given as a weighted graph with 160 nodes (148 cortical and 12 subcortical ROIs) from Destrieux atlas [1] and the weights denote the number of white matter fiber tracts connecting different ROIs. The dataset is composed of 1824 subjects within Control (CN, N=844), Early and Late Mild Cognitive Impairment (EMCI, N=490 and LMCI, N=250), and AD (N=240) groups.
Preliminaries. A simplicial complex comprises simplices, representing objects in varying dimensions within topological space, such as nodes (0-simplex), edges (1-simplex), triangles (2-simplex), and higher-dimensional counterparts. The mapping of simplices in the p-th dimension to their (p-1)-th dimensional boundaries is facilitated by a boundary matrix, a matrix form of the boundary operator. This boundary matrix plays an important role in defining the Hodge Laplacian, enhancing the representation of higher-order graph structures.
Method. The proposed method is composed of two components: 1) graph transformation of adjacency matrix to Hodge 1-Laplacian, and 2) edge-wise graph convolution using the Hodge 1-Laplacian (Fig. 1a). The Hodge 1-Laplacian is defined through the 1-simplex boundary matrix (i.e., the incidence matrix), capturing topological features associated with 1-simplices not initially discernible in the original graph form. Consequently, utilizing Hodge 1-Laplacian for spatial graph convolution not only provides the connectivity over edges, but also assigns different weights on adjacent edges based on the graph topology (Fig. 1b).
4-way graph classification on Control, EMCI, LMCI and AD was conducted via 5-fold cross validation. The performance was measured using average accuracy, Macro-(precision, recall, and F1-score), and compared with various baseline methods.
Preliminaries. A simplicial complex comprises simplices, representing objects in varying dimensions within topological space, such as nodes (0-simplex), edges (1-simplex), triangles (2-simplex), and higher-dimensional counterparts. The mapping of simplices in the p-th dimension to their (p-1)-th dimensional boundaries is facilitated by a boundary matrix, a matrix form of the boundary operator. This boundary matrix plays an important role in defining the Hodge Laplacian, enhancing the representation of higher-order graph structures.
Method. The proposed method is composed of two components: 1) graph transformation of adjacency matrix to Hodge 1-Laplacian, and 2) edge-wise graph convolution using the Hodge 1-Laplacian (Fig. 1a). The Hodge 1-Laplacian is defined through the 1-simplex boundary matrix (i.e., the incidence matrix), capturing topological features associated with 1-simplices not initially discernible in the original graph form. Consequently, utilizing Hodge 1-Laplacian for spatial graph convolution not only provides the connectivity over edges, but also assigns different weights on adjacent edges based on the graph topology (Fig. 1b).
4-way graph classification on Control, EMCI, LMCI and AD was conducted via 5-fold cross validation. The performance was measured using average accuracy, Macro-(precision, recall, and F1-score), and compared with various baseline methods.
Results:
Experimental Results. Our method outperformed conventional graph classification methods [4], spatial and spectral GNNs [5,6], and edge convolution method [9] in all evaluation measures (Fig. 2A). Also, the significant edges depicted from the AD analysis exhibited consistency with prior works of AD, highlighting connectomes within subcortical regions, temporal lobe, and frontal lobe (Fig. 2B,C) [3]. Interestingly, some of the depicted edges showed symmetry found in both hemispheres, such as pallidum-putamen and amygdala-hippocampus connectomes, which are known to play crucial roles in the development of AD [7,8].
Conclusions:
We proposed a novel graph edge-learning framework, Hodge-GNN, to extract edge-wise relationships within the spatial domain of graphs via Hodge 1-Laplacian. Hodge-GNN conducts graph convolution on edges directly, enabling an accurate classification of AD stages. The validation experiment proved effectiveness even in scenarios lacking node-wise measurements, a common reliance in most GNN methods, accompanied by interpretability that delineates specific connectomes and ROIs for effective AD analysis.
Modeling and Analysis Methods:
Classification and Predictive Modeling 1
Connectivity (eg. functional, effective, structural) 2
Keywords:
Degenerative Disease
Machine Learning
Other - Alzheimer’s Disease
1|2Indicates the priority used for review
Provide references using author date format
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