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Understanding Graph Isomorphism Network for rs-fMRI Functional Connectivity Analysis
Byung-Hoon Kim, Jong Chul Ye
TL;DR
Existing GNN applications to fMRI face difficulty explaining classifications in a neuroscientifically interpretable way. This paper develops a GIN-based framework that recasts GIN as a graph-space CNN, enabling input-layer Grad-CAM with one-hot node encoding; sex classification on rs-fMRI produced accurate predictions and salient regions corresponding to prior neuroimaging evidence.
Problem
Existing GNN applications to fMRI face difficulty explaining classification results in a neuroscientifically interpretable way.
Method
The framework constructs brain graphs from region labels and functional connectivity, trains a GIN for phenotype classification, and backpropagates through it for saliency mapping.
Results
84.61% accuracy, 86.19% precision, and 86.81% recall were obtained for sex classification from rs-fMRI data.
Takeaways & Limitations
The saliency maps highlighted DMN involvement and showed robustness and mapping sensitivity relative to a CAM-based method.
Takeaways & Limitations
Demographic factors were not thoroughly controlled, and salient regions were selected using a heuristic top-5-percentile cutoff.
Abstract
from arXiv · showhide
Graph neural networks (GNN) rely on graph operations that include neural network training for various graph related tasks. Recently, several attempts have been made to apply the GNNs to functional magnetic resonance image (fMRI) data. Despite recent progresses, a common limitation is its difficulty to explain the classification results in a neuroscientifically explainable way. Here, we develop a framework for analyzing the fMRI data using the Graph Isomorphism Network (GIN), which was recently proposed as a powerful GNN for graph classification. One of the important contributions of this paper is the observation that the GIN is a dual representation of convolutional neural network (CNN) in the graph space where the shift operation is defined using the adjacency matrix. This understanding enables us to exploit CNN-based saliency map techniques for the GNN, which we tailor to the proposed GIN with one-hot encoding, to visualize the important regions of the brain. We validate our proposed framework using large-scale resting-state fMRI (rs-fMRI) data for classifying the sex of the subject based on the graph structure of the brain. The experiment was consistent with our expectation such that the obtained saliency map show high correspondence with previous neuroimaging evidences related to sex differences.
1 INTRODUCTION
The paper frames brain functional connectivity as graph data and positions GNNs, especially GIN, as tools for graph classification of fMRI phenotypes. It addresses the need for interpretable classification by linking GIN operations to CNN-based saliency mapping.
- Brain graphs: Brain functional connectivity can be represented as a graph whose nodes are regions of interest and whose edges encode connectivity.Classical analyses compute graph metrics such as efficiency, path length, and small-worldedness.
- Graph neural networks: GNNs aggregate neighborhood features across layers and apply a readout function to obtain a graph-level representation for classification.After k aggregation layers, each node incorporates information from its k-hop neighborhood.
- Applications to fMRI: Prior studies applied GNNs to classify phenotypic status from brain functional networks, sometimes combining imaging and non-image phenotypic data.These applications motivate further analysis of GNNs for fMRI data.
- Motivation: GIN was revisited because it offers powerful graph classification, while direct calculation of graph saliency maps remained unclear.The paper treats this interpretability gap as a central motivation.
- Proposed perspective: GIN can be viewed as a dual representation of CNNs in graph space, with the adjacency matrix acting as a generalized shift operation.This perspective supports transferring CNN saliency techniques to GIN.
- Validation: The proposed framework uses GIN to classify subject sex from rs-fMRI graph structure and reports more accurate classification with more interpretable saliency maps.The saliency maps provide insights related to sex differences in resting-state fMRI.
2 THEORY
The theory presents GIN as a two-tab CNN equivalent on graph space, replacing the CNN shift matrix with the graph adjacency matrix. This equivalence motivates input-layer Grad-CAM with one-hot node encoding for identifying salient brain regions.
- GIN formulation: The paper formulates GIN as a graph-classification operation and derives a matrix representation involving the adjacency matrix and learnable channel weights.The operation is applied across successive layers, with c^(k) defined from the layer-specific parameter ϵ^(k).
- GIN formulation: GIN differs from GCN through the use of c^(k)I + A instead of normalized adjacency, and can therefore be interpreted as a CNN-like graph operation.The paper also characterizes GIN as an extension of GCN using the unnormalized graph Laplacian.
- Dual representation: Theorem 1 states that a GIN iteration is a dual representation of a CNN without pooling layers using a two-tab filter, with adjacency serving as the graph-space shift operation.The derivation identifies the adjacency matrix as the key replacement for the conventional CNN shift matrix.
- Saliency mapping: The CNN analogy permits CNN saliency techniques to be applied to GIN for visualizing important brain regions.The paper proposes Grad-CAM rather than CAM because Grad-CAM does not require a global average pooling layer.
- Saliency mapping: For brain-region attribution, the meaningful Grad-CAM map is calculated at the input layer, where graph nodes use one-hot encoding.This setup links input-node contributions directly to the final classification.
3 MATERIALS AND METHODS
The study applies GIN to rs-fMRI sex classification by constructing sparse functional-connectivity graphs, using one-hot ROI encodings, and adding Infomax regularization. Saliency maps are computed and compared with a CAM-based method to interpret brain regions associated with each class.
- Pipeline: The analysis pipeline applies GIN to rs-fMRI graphs for classifying subjects’ sex and providing neuroscientific interpretation.The proposed pipeline is schematically illustrated for rs-fMRI graph classification and analysis.
- Data: The HCP rs-fMRI data were preprocessed, filtered for framewise displacement, and reduced to 942 scans from 1094 subjects.Scans with framewise displacement over 0.3 mm were discarded, leaving 531 female and 411 male scans.
- Graph construction: Each graph uses 400 Schaefer cortical parcellations as nodes, represented by one-hot vectors encoding semantic region labels.The node encoding uses ROI labels rather than the underlying fMRI signal.
- Graph construction: Edges are formed from pairwise Pearson correlations between ROI mean time series, retaining the top M-percentile connections to produce undirected unweighted graphs.The connectivity matrix is thresholded by sparsity so selected entries become connected edges.
- Saliency mapping: Subject-level saliency maps are averaged and normalized, focusing on the top 5-percentile regions, while robustness and mappings are compared with CAM-based saliency.The top 5-percentile corresponds to 20 of the 400 regions.
4 RESULTS
The proposed GIN achieved the strongest reported classification performance and showed robust, interpretable saliency maps. Salient regions included frontal, cingulate, temporal, parietal, visual, and somatomotor areas, with overlaps and differences relative to CAM-based maps.
- Classification performance: 84.61% accuracy was achieved by the proposed method, compared with 83.98% for the baseline GCN-based method.Other recent non-GNN approaches reported lower classification performance than the baseline.
- Hyperparameter analysis: 30% graph sparsity produced the best performance, and the final GIN used 5 layers with 64 hidden units per layer.The final configuration also used 0.5 dropout at the final linear layer and regularization coefficient λ = 0.05.
- Node embeddings: Centroid-coordinate and mean-BOLD node embeddings produced significantly lower classification accuracy than the one-hot ROI embedding.The study also visualized the corresponding latent spaces with t-SNE and computed silhouette scores.
- Saliency robustness: 92.5% and 87.5% top-region matches were obtained for female and male classes with five-fold aggregated saliency maps.One-fold aggregation yielded 63.5% and 65.5% matches, respectively, while CAM-based mapping was lower under the same conditions.
- Female-class maps: Female-class saliency included prefrontal, orbitofrontal, cingulate, frontal opercular, temporal, parietal, and visual regions.The reported female salient regions were identified among the top 5-percentile values.
- Male-class maps: Male-class saliency included prefrontal, orbitofrontal, posterior cingulate, precuneus, temporal, intraparietal, visual, and somatomotor regions.The default mode network was predominant for the male class as for the female class.
- Method comparison: CAM-based maps overlapped with the proposed method in regions including PFC, orbitofrontal, cingulate, PCC, precuneus, and temporal/parietal areas.The most notable difference was the absence of regions from the SMN and VN in the CAM-based maps.
5 DISCUSSION
The discussion reports that the GIN framework combines competitive sex classification with interpretable saliency maps that correspond to established and emerging rs-fMRI sex-difference findings. It also identifies demographic controls and saliency thresholds as important limitations.
- Framework: The framework classifies sex from rs-fMRI while providing saliency maps for interpreting brain regions associated with the decision.The proposed analysis constructs graphs, trains a GIN, and backpropagates through it to visualize classification-related regions.
- Classification performance: 84.61% accuracy, 86.19% precision, and 86.81% recall were achieved for sex classification from rs-fMRI data.The performance was reported as at least comparable to recent methods using the HCP dataset.
- Neuroimaging interpretation: DMN regions were most prominent for classifying both female and male subjects, with saliency proportions similar to previous sex-classification evidence.DMN regions comprised 30% of salient regions for the female class and 35% for the male class, compared with 35% among a prior study’s top twenty regions.
- Neuroimaging interpretation: Female saliency was left-lateralized, whereas male saliency was right-lateralized in the proposed mapping results.Female salient regions were left 65% versus right 35%; male regions were left 45% versus right 55%.
- Saliency comparison: Compared with CAM, the proposed saliency method showed greater robustness and mapping sensitivity, identifying SMN and VN involvement that CAM did not identify.The authors note that evidence for SMN and VN sex differences is less established than evidence for DMN differences.
- Limitations: Demographic factors were not thoroughly controlled, and salient regions were selected using a heuristic top-5-percentile threshold.The authors identify age, handedness, fluid intelligence, and other characteristics as potentially relevant, and call for more data-driven significance determination.
Expressive explanation of the GIN operation
The GIN operation aggregates node features and neighborhoods before applying an MLP and ReLU, but linearly dependent node features can reduce discriminative power. One-hot ROI encoding avoids this issue by making input features orthogonal and supports interpretable saliency mapping.
- Aggregation: GIN first aggregates each node’s scaled feature with the sum of its neighboring features, using the learnable parameter ϵ.The example sets ϵ^(0) = 0.1 before mapping the aggregated feature matrix through the MLP.
- Transformation: The aggregated feature matrix is passed through an MLP and then a ReLU nonlinearity to produce the next-layer node features.The same operations are applied to node features at each GIN layer.
- Discriminative power: Linearly dependent node features reduce GIN’s discriminative power because sum aggregation can become non-injective.The GIN’s WL-level expressiveness requires injective aggregate, combine, and readout mappings.
- Discriminative power: In the example, two graphs produce identical first-layer node embeddings, making their first-node embeddings indistinguishable regardless of the MLP.This occurs when the relevant input feature vectors are linearly dependent.
- One-hot encoding: One-hot encoding assigns each ROI an orthogonal, linearly independent feature vector, improving practical discriminability and interpretability of Grad-CAM maps.The encoding makes separate regions distinguishable in the input representation.
TABLES AND FIGURES
The paper presents tables and figures covering the GIN-based analysis pipeline, model comparisons, hyperparameter and embedding studies, saliency robustness, and salient brain regions.
- The tables cover sex-classification method comparisons, hyperparameter tuning, node-feature embeddings, saliency robustness, and top 5-percentile salient regions for both methods.
- Figure 1 schematically illustrates the Graph Isomorphism Network-based resting-state fMRI analysis.
- Figure 2 compares the shift operation in a classical CNN with a GIN, where the adjacency matrix defines the graph-space shift operation.
- Figure 4 examines classification accuracy as a function of edge sparsity, while Figure 5 visualizes latent-space embeddings with t-SNE and reports mean silhouette scores.
- Figures 6 and 7 visualize salient brain regions identified by the proposed method and the CAM-based method, respectively.