HL-HGAT: A Hodge-Laplacian and Attention Mechanism Approach for Brain Functional Network

1876 

Abstract Submission 

Jinghan Huang¹, Anqi Qiu^1,2,3

¹Department of Biomedical Engineering, National University of Singapore, Singapore, Singapore, ²Department of Health Technology and Informatics, Hong Kong Polytechnic University, Kowloon, Hong Kong, ³Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD

Jinghan Huang  
Department of Biomedical Engineering, National University of Singapore
Singapore, Singapore

Anqi Qiu  
Department of Biomedical Engineering, National University of Singapore|Department of Health Technology and Informatics, Hong Kong Polytechnic University|Department of Biomedical Engineering, Johns Hopkins University
Singapore, Singapore|Kowloon, Hong Kong|Baltimore, MD

Graph neural networks (GNNs) effectively model complex data relationships and are crucial in fMRI analysis for cognitive and mental disorder studies [1]. Yet, conventional GNNs often overlook complex interrelations beyond node-centric views [2]. Addressing this, our Hodge-Laplacian Heterogeneous Graph Attention Network (HL-HGAT) redefines graphs as simplicial complexes, capturing multi-dimensional data interplay on any k-simplex. We benchmarked HL-HGAT against leading GNN models such as GAT [3], BrainGNN [4], dGCN [5], and Hypergraph NN [6] using the ABCD and OASIS-3 datasets. Our results highlight that HL-HGAT's attention maps offer meaningful insights into neural circuits associated with general intelligence and brain age.

HL-HGAT combines Hodge-Laplacian (HL) operators and attention mechanisms across k-simplices. Its core consists of three innovative components: HL convolutional filters (HL-filters), multi-simplicial interaction (MSI), and simplicial attention pooling (SAP) operators. The HL-filters, operating within the spectral domain of the k-th HL operators, are enhanced by a novel polynomial approximation method, offering computational efficiency and spatial localization. Although HL-filters primarily operate on specific-dimensional simplices, it is essential to acknowledge that signals on simplices of different dimensions can exhibit intricate interconnections. The MSI module enables signal interaction across distinct dimensional simplices by a simplicial projection operator, which allows signals from k1-simplices to be transformed into k2-simplices, facilitating their fusion and thus facilitating the learning of their interactions. Finally, SAP is designed for efficient spatial dimension reduction of simplices and information pooling. The pooling operator is defined by coarsening the k-simplice and consolidating features associated with these simplices using attention mechanisms. These mechanisms encompass self-attention and cross-attention facilitated through simplicial projection operators and transformers. The simplicial transformers determine the importance of each simplex by learning its weight while gathering signals from its topologically connected simplices, thus evaluating their relevance to a downstream task. For the specific application on brain networks, the k1-simplex and k2-simplex denote node and edge, respectively.

We employed two functional MRI datasets, the Adolescent Brain Cognitive Development Study (ABCD, n=7,693) [7] and Open Access Series of Imaging Studies (OASIS-3, n=1,978, https://www.oasis-brains.org/), to predict intelligence and brain age. Our brain graphs utilized 268 regions of interest (ROIs) as nodes [8], linked by edges based on Pearson's correlation across functional time series. Fig. 2(A,B) showcases HL-HGAT's superior performance over baseline models, establishing it as a leading solution in the OASIS and ABCD datasets. For OASIS, HL-HGAT outperforms baseline GNNs like GAT, BrainGNN, and dGCN in node signal processing (p<0.01), and eclipses Hypergraph NN in edge signal accuracy (p=0.02). ABCD dataset results further confirm HL-HGAT's lower mean absolute errors (MAE) compared to the aforementioned models (p<0.01). The last four columns in Fig. 2(A,B) indicate that HL-HGAT's enhanced models (M1 to M4) improve predictive accuracy. Fig. 2(C,D) focuses on the most influential functional connectivities, particularly within the hippocampus and amygdala for brain age, and between prefrontal and parietal regions for intelligence prediction, in line with existing neuroscience research [9-10].

HL-HGAT stands as a substantial advancement in GNN technology. Its proficiency in handling heterogeneous signals, modeling complex interconnections across simplicial dimensions, and ensuring computational efficiency positions it as a versatile tool for brain fMRI analysis.

Early life, Adolescence, Aging

Activation (eg. BOLD task-fMRI)

Connectivity (eg. functional, effective, structural)

Methods Development ¹

BOLD fMRI ²

Aging

Cognition

Development

FUNCTIONAL MRI

Machine Learning

Open-Source Code

Other - Graph neural networks