Graph Autoencoders for Embedding Learning in Brain Networks and Major Depressive Disorder Identification

TL;DR

This work introduces a graph autoencoder framework (GAE-FCNN) built on graph convolutional networks to embed rs-fMRI brain networks into low-dimensional representations for MDD identification. By estimating high-dimensional functional connectivity with Ledoit-Wolf shrinkage, constructing subject-specific graphs, and learning graph embeddings in both unsupervised and supervised settings, the approach achieves superior brain network classification performance when combined with a deep FCNN. The model yields interpretable, high-order connectivity patterns that differentiate MDD from healthy controls beyond what raw FC captures, and demonstrates strong potential for graph-based diagnostics in neuropsychiatric disorders. The method is applicable to other modalities and disorders, and highlights the value of preserving graph topology in brain connectome analysis for clinical impact.

Abstract

Brain functional connectivity (FC) reveals biomarkers for identification of various neuropsychiatric disorders. Recent application of deep neural networks (DNNs) to connectome-based classification mostly relies on traditional convolutional neural networks using input connectivity matrices on a regular Euclidean grid. We propose a graph deep learning framework to incorporate the non-Euclidean information about graph structure for classifying functional magnetic resonance imaging (fMRI)-derived brain networks in major depressive disorder (MDD). We design a novel graph autoencoder (GAE) architecture based on the graph convolutional networks (GCNs) to embed the topological structure and node content of large-sized fMRI networks into low-dimensional latent representations. In network construction, we employ the Ledoit-Wolf (LDW) shrinkage method to estimate the high-dimensional FC metrics efficiently from fMRI data. We consider both supervised and unsupervised approaches for the graph embedding learning. The learned embeddings are then used as feature inputs for a deep fully-connected neural network (FCNN) to discriminate MDD from healthy controls. Evaluated on two resting-state fMRI (rs-fMRI) MDD datasets, results show that the proposed GAE-FCNN model significantly outperforms several state-of-the-art methods for brain connectome classification, achieving the best accuracy using the LDW-FC edges as node features. The graph embeddings of fMRI FC networks learned by the GAE also reveal apparent group differences between MDD and HC. Our new framework demonstrates feasibility of learning graph embeddings on brain networks to provide discriminative information for diagnosis of brain disorders.

Figures (7)

• Figure 1: The architecture of proposed GAE-FCNN framework for functional brain network classification. (a) Unsupervised model. The model consists of two components: A GAE employs a GCN-based encoder to encode fMRI connectome data (graph structure $\mathbf{A}$ & node content $\mathbf{X}$) into latent representations $\mathbf{Z}$ on which a decoder is used to reconstruct the graph information. A deep FCNN performs network-level classification to discriminate MDD patients and HCs based on the learned representations. (b) Supervised model. The GCN encoder combined with FCNN leverages on class labels to learn network representations and performs network classification in an end-to-end framework.
• Figure 2: The learning curve as a function of training epochs and reconstruction loss of the GAE model.
• Figure 3: Effect of two FC network thresholding strategies with varying threshold values on MDD classification accuracy of the unsupervised GAE-FCNN model. (a) Proportional thresholding. (b) k-nearest neighbor graph. Network adjacency matrix: LDW. Node feature: LDW-FC.
• Figure 4: Visualization of $116 \times 16$ network embedding matrices $\mathbf{Z}$ (averaged over subjects) learned by the GCN-GAE from rs-fMRI functional networks. (a) HC subjects. (b) MDD subjects. (c) The between-group variance i.e., $\boldsymbol{\sigma}^{2}_\text{b} = \left(\bar{\mathbf{Z}}_\text{HC}-\bar{\mathbf{Z}}\right)^{2} n_\text{HC} + \left(\bar{\mathbf{Z}}_\text{MDD}-\bar{\mathbf{Z}}\right)^{2} n_\text{MDD}$ where $\bar{\mathbf{Z}}_\text{HC}$ and $\bar{\mathbf{Z}}_\text{MDD}$ are mean embeddings of each group, $\bar{\mathbf{Z}}$ is mean embeddings over both groups, $n_\text{HC}$ and $n_\text{MDD}$ are the number of subjects in each group.
• Figure 5: Differences in connectivity pattern between MDD and HC as revealed by raw FC from rs-fMRI data (Top) and high-order FC derived from GAE-learned node embeddings (Bottom). Group mean FC maps for HC (left) and MDD (middle) subjects, and their differences (MDD - HC) (right). The group differences shown are significantly different from zero at level $\alpha$ = 0.05 using an independent two-sample t-test.