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Learning Multi-resolution Graph Edge Embedding for Discovering Brain Network Dysfunction in Neurological Disorders

Xin Ma, Guorong Wu, Seong Jae Hwang, Won Hwa Kim

TL;DR

Multi-resolution Edge Network (MENET) is proposed to detect disease-specific connectomic benchmarks with high discrimination power across diagnostic categories and devise a graph learning framework to jointly select discriminative edges and assign diagnostic labels for graphs.

Abstract

Tremendous recent literature show that associations between different brain regions, i.e., brain connectivity, provide early symptoms of neurological disorders. Despite significant efforts made for graph neural network (GNN) techniques, their focus on graph nodes makes the state-of-the-art GNN methods not suitable for classifying brain connectivity as graphs where the objective is to characterize disease-relevant network dysfunction patterns on graph links. To address this issue, we propose Multi-resolution Edge Network (MENET) to detect disease-specific connectomic benchmarks with high discrimination power across diagnostic categories. The core of MENET is a novel graph edge-wise transform that we propose, which allows us to capture multi-resolution ``connectomic'' features. Using a rich set of the connectomic features, we devise a graph learning framework to jointly select discriminative edges and assign diagnostic labels for graphs. Experiments on two real datasets show that MENET accurately predicts diagnostic labels and identify brain connectivities highly associated with neurological disorders such as Alzheimer's Disease and Attention-Deficit/Hyperactivity Disorder.

Learning Multi-resolution Graph Edge Embedding for Discovering Brain Network Dysfunction in Neurological Disorders

TL;DR

Multi-resolution Edge Network (MENET) is proposed to detect disease-specific connectomic benchmarks with high discrimination power across diagnostic categories and devise a graph learning framework to jointly select discriminative edges and assign diagnostic labels for graphs.

Abstract

Tremendous recent literature show that associations between different brain regions, i.e., brain connectivity, provide early symptoms of neurological disorders. Despite significant efforts made for graph neural network (GNN) techniques, their focus on graph nodes makes the state-of-the-art GNN methods not suitable for classifying brain connectivity as graphs where the objective is to characterize disease-relevant network dysfunction patterns on graph links. To address this issue, we propose Multi-resolution Edge Network (MENET) to detect disease-specific connectomic benchmarks with high discrimination power across diagnostic categories. The core of MENET is a novel graph edge-wise transform that we propose, which allows us to capture multi-resolution ``connectomic'' features. Using a rich set of the connectomic features, we devise a graph learning framework to jointly select discriminative edges and assign diagnostic labels for graphs. Experiments on two real datasets show that MENET accurately predicts diagnostic labels and identify brain connectivities highly associated with neurological disorders such as Alzheimer's Disease and Attention-Deficit/Hyperactivity Disorder.

Paper Structure

This paper contains 14 sections, 1 theorem, 12 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Proposed Method
  4. Multi-resolution Graph Edge Transform
  5. Efficient Graph Matrix Transform
  6. Network Architecture
  7. Training MENET
  8. Experiments
  9. Datasets
  10. Experimental Settings
  11. Structural Brain Connectivity Analysis on ADNI
  12. Functional Brain Connectivity Analysis on ADHD
  13. Discussions on Convergence of Scales
  14. Conclusion

Key Result

lemma thmcounterlemma

(Graph Laplacian Admissibility Condition) Given a kernel dependent normalization constant $C_k = \int_0^\infty \frac{k(x)^2}{x}dx < \infty$, the original graph Laplacian $\mathcal{L}$ can be perfectly reconstructed via the inverse transformation.

Figures (4)

  • Figure 1: Example of multi-resolution representation of brain connectivity. 1) original network, 2)-4) filtered network at $s= 0.3, 0.8, 1.8$. Sparsity of the network increases and nodal degree decreases (red to blue) as the scale changes.
  • Figure 2: Overall architecture of MENET. A graph matrix is transformed to yield multi-resolution representations, and then fully connected (FC) DNN is applied at the end. Error is backpropagated to train the weights $\mathbf{W^h}$ and update the scales $\mathbf{s}$ to obtain the optimal representations.
  • Figure 3: Top-10 Connectivities from ADNI (Left) and ADHD-200 (Right) Analyses. Edge thickness denotes average trained edge weight and node color denotes its degree.
  • Figure 4: Convergence of scales w.r.t. training epoch. Top: ADNI, Bottom: ADHD-200.

Theorems & Definitions (2)

  • lemma thmcounterlemma
  • proof