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Interpretable Information-Decomposed Brain Graph Learning for fMRI-based Disease Diagnosis

Dengyi Zhao, Zhiheng Zhou, Zihan Wang, Guiying Yan, Xingqin Qi

arXiv:2608.20380v1q-bio.NCcs.LG

TL;DR

Traditional correlation-based brain graphs may miss how information is shared across regions because they reduce interactions to edge weights. IID-GCN decomposes rs-fMRI interactions into redundancy, uniqueness, and synergy graphs and integrates them with an interpretable multi-channel GNN. Across three datasets, it consistently captures complementary diagnostic information beyond traditional functional connectivity.

  • Problem

    Correlation-based functional connectivity captures co-fluctuation strength but may obscure redundancy, uniqueness, and synergy relevant to disease-related brain information organization.

  • Method

    IID-GCN applies partial entropy decomposition to binary rs-fMRI brain-state sequences, then jointly models redundancy, uniqueness, and synergy graphs with an interpretable multi-channel GNN.

  • Results

    Across ADNI, PPMI, and ABIDE, IID-GCN achieves accuracies of 73.9%, 70.7%, and 65.1%, outperforming the strongest baselines by 3.1%, 6.5%, and 2.4%, respectively.

  • Takeaways & Limitations

    Information-decomposed brain graphs provide complementary diagnostic descriptions beyond traditional correlation-based connectivity and support interpretable analysis of brain information organization.

Abstract

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Resting-state functional magnetic resonance imaging (rs-fMRI) has enabled non-invasive mapping of functional brain interactions for computer-aided diagnosis, yet most existing approaches reduce inter-regional relationships to correlation-based edge weights. Such representations capture co-fluctuation strength but obscure how information is shared across brain regions. Because brain disorders may disrupt not only connectivity strength but also the organization of redundancy, uniqueness and synergy, traditional functional connectivity may miss disease-relevant information structures. Here we introduce IID-GCN, an interpretable graph learning framework that decomposes rs-fMRI interactions into redundancy, uniqueness and synergy graphs using partial entropy decomposition. These information-specific graphs separately characterize shared, region-specific and jointly emergent components of brain activity. A multi-channel graph convolutional network then integrates the decomposed graphs through edge recalibration, cross-information interaction, ROI-attention readout and channel-attentive fusion. Across three datasets, IID-GCN consistently captures complementary diagnostic information beyond traditional functional connectivity. The learned information profiles reveal disorder-specific patterns of altered redundancy, uniqueness and synergy, suggesting that brain diseases reshape functional information organization rather than merely changing connection strength. These results establish information-decomposed brain graphs as an interpretable representation for rs-fMRI-based diagnosis. Our code is available at https://github.com/Zdy12/IID-GCN.

I. INTRODUCTION

The paper argues that correlation-based brain graphs compress distinct information-sharing modes into single edge weights, motivating an interpretable information-decomposed alternative. IID-GCN constructs and jointly learns redundancy, uniqueness, and synergy graphs, with evaluation across three public neuroimaging datasets.

  • Correlation-based functional connectivity reduces each ROI relationship to a scalar co-fluctuation strength, obscuring distinct information-sharing modes.
  • IID-GCN applies partial entropy decomposition to binary rs-fMRI brain-state sequences, producing subject-specific redundancy, uniqueness, and synergy graphs.
  • The proposed multi-channel GCN jointly models the three information graphs with edge recalibration, cross-information interaction, ROI attention, soft grouping, and channel-attentive fusion.
  • The study evaluates IID-GCN on three public datasets covering neurodegenerative and neurodevelopmental disorders, including classification, ablation, robustness, threshold-sensitivity, and interpretability analyses.
  • The paper presents information-decomposed rs-fMRI graphs as a representation beyond traditional functional connectivity for interpretable brain-disorder diagnosis.

B. Graph Neural Networks for Brain Graph Learning

This section motivates replacing single connectivity matrices with three information-specific graphs. Binary brain-state sequences and partial entropy decomposition quantify shared, region-specific, and jointly emergent information between ROI pairs for multi-channel graph learning.

  • Existing brain graph methods mainly improve learning architectures while retaining correlation-based inputs, collapsing heterogeneous information-sharing components into one edge weight.
  • Regional rs-fMRI signals are standardized and converted into binary brain-state sequences before entropy-based information decomposition.
  • Partial entropy decomposition separates pairwise joint entropy into redundancy, uniqueness, and synergy atoms.
  • Applying PED across ROI pairs yields subject-specific graphs representing shared, region-specific, and jointly emergent information beyond correlation-based connectivity.
  • Top-k sparsification retains the strongest connections for each ROI in each information channel to reduce weak noisy edges and improve graph sparsity.

C. Residual Edge Gate

The residual edge gate adaptively recalibrates connections in each information channel while preserving the original PED-derived graph as the model’s starting structure.

  • The residual edge gate learns continuous channel-specific edge modulation scores to upweight or down-weight graph connections during training.
  • For each redundancy, uniqueness, or synergy channel, the raw gate uses a learnable scaling parameter and symmetric zero-diagonal modulation matrix.
  • The recalibrated adjacency combines the original graph with bounded channel-specific residual modulation through element-wise multiplication.
  • Initializing the residual coefficient at zero makes training begin from the original PED-derived graph and learn task-driven deviations gradually.

D. Information-Specific Graph Convolution Layer

IID-GCN encodes redundancy, uniqueness, and synergy graphs in separate graph-convolution branches to preserve channel-specific functional organization during representation learning.

  • Each information-specific graph is encoded by an independent graph-convolution branch after edge-level recalibration.
  • Graph convolution aggregates information from graph-defined neighbors to capture local and higher-order connectivity patterns.
  • Separate branches allow channel-specific functional organization to be learned without prematurely mixing heterogeneous information components.
  • Each channel begins with a channel-specific input projection and symmetric normalization of its recalibrated adjacency matrix.
  • Two graph-convolutional layers are used in each information channel.

E. Mutual Cross-Attention-Based Information Fusion

IID-GCN models complementary relationships among redundancy, uniqueness, and synergy through mutual cross-attention. Each target channel preserves its own information while selectively incorporating node-level information from the other channels.

  • Mutual cross-attention models complementary relationships among redundancy, uniqueness, and synergy channels.
  • For each target channel, its node representation serves as the query while another information channel supplies complementary source information.
  • Attention weights quantify how ROIs in a target channel attend to ROIs in a complementary source channel.
  • The refined channel representations preserve original information while incorporating cross-attended information from the other two channels.

F. Information-Guided Graph Readout and Prediction

IID-GCN converts refined information-channel node representations into graph-level embeddings using multi-level readouts, then adaptively fuses channels for diagnostic prediction.

  • Refined node representations from redundancy, uniqueness, and synergy channels are aggregated into graph-level representations for disease prediction.
  • The readout combines global pooling, ROI-attention readout, and soft subnetwork-level grouping to capture complementary graph-level information.
  • Global mean and max pooling summarize the overall distribution of ROI representations.
  • ROI attention identifies disease-relevant regions and provides explanations of which ROIs are emphasized in each information channel.
  • Soft node grouping captures subnetwork-level organization through a learned assignment matrix and latent brain groups.
  • Each channel embedding combines multiple readout components, and channel attention weights quantify the relative contributions of redundancy, uniqueness, and synergy to prediction.
  • The fused graph-level representation is classified into diagnostic probabilities, integrating ROI-level patterns, latent subnetworks, and information channels.

G. Training Objective

IID-GCN is trained under supervised classification using cross-entropy loss, with predicted class probabilities compared across diagnostic classes.

  • IID-GCN uses supervised training with a cross-entropy classification loss.
  • The predicted probability bpi,m denotes the probability that subject i belongs to diagnostic class m.

A. Datasets and Preprocessing

IID-GCN is evaluated on three public neuroimaging datasets using matched baselines, cross-validation, and multiple performance measures. It achieves the strongest reported classification performance while testing information-theoretic features and model components.

  • Datasets and Evaluation: The evaluation covers ADNI, PPMI, and ABIDE, with comparisons against traditional classifiers, general-purpose GNNs, and brain-network-oriented deep models.The protocol measures accuracy, precision, recall, and F1-score, using weighted averages for multi-class tasks.
  • Datasets and Evaluation: 10-fold cross-validation uses an 8:1:1 training-validation-test split, retaining the model with the highest validation F1-score.Results are reported as mean ± standard deviation across folds.
  • Performance Comparison: 73.9%, 70.7%, and 65.1% accuracy on ADNI, PPMI, and ABIDE, respectively, outperform the strongest baselines by 3.1%, 6.5%, and 2.4%.Similar improvements are reported for precision, recall, and F1-score.
  • Performance Comparison: IID-GCN consistently outperforms traditional classifiers, generic GNNs, and brain-network-oriented deep models, achieving the highest F1-scores on all datasets.The results are attributed to complementary diagnostic signals from separately modeled redundancy, uniqueness, and synergy.
  • Information-Theoretic Features: The combined redundancy–uniqueness–synergy representation performs best overall, while individual components show dataset-dependent strengths.Uniqueness performs well on ADNI, redundancy on PPMI, and the combined representation gives more balanced results on ABIDE.
  • Model Components: The full model consistently performs best in module-level ablations, with soft node grouping and ROI attention especially important on ADNI.The ablated modules include residual edge gating, mutual cross-attention, ROI attention readout, soft node grouping readout, and channel attention.

F. Hyperparameter Analysis

IID-GCN is analyzed across graph sparsity, latent brain-group size, cross-information interactions, and channel contributions. Moderate graph and group configurations are favored, while learned attention patterns vary by diagnosis and dataset.

  • Retained Neighbor Number: Moderate graph sparsity is favored: stable performance occurs around k = 20 on ADNI and k = 30 on PPMI and ABIDE.Very small k may discard informative connections, whereas overly large k can introduce weak or noisy information-theoretic edges.
  • Latent Brain Group Number: Performance improves as the latent brain group number K increases from very small values to a moderate range, but excessive K can yield redundant or unstable representations.The best or near-best results are typically obtained with a moderate number of latent groups.
  • Cross-Information Interaction: Cross-attention maps are non-uniform and diagnosis-dependent, with AD and MCI deviating more from uniform attention than CN, especially for redundancy and uniqueness directions.Similar diagnosis-dependent patterns are observed on PPMI and ABIDE.
  • Cross-Information Interaction: The learned attention patterns indicate diagnosis-specific information exchange pathways beyond traditional connectivity strength.The finding is reported across the diagnostic groups and datasets examined.
  • Information-Channel Contributions: Synergy receives the highest attention on ADNI and PPMI, whereas uniqueness dominates on ABIDE.On PPMI, redundancy contributes the least; on ABIDE, uniqueness is significantly higher than redundancy and synergy.
  • Information-Channel Contributions: The dominant information channel is disease-dependent, supporting adaptive channel-attentive fusion rather than equal treatment of all components.Redundancy, uniqueness, and synergy therefore contribute differently across disorders.

2) Brain-region importance analysis:

IID-GCN identifies dataset-specific brain regions and latent subnetworks through information-specific channels, revealing disorder- and disease-stage-related organization of redundancy, uniqueness, and synergy.

  • ROI importance: ADNI importance maps emphasize motor, precuneus, cingulate, and precentral regions, consistent with altered synergy-related information organization.
  • ROI importance: ABIDE importance maps emphasize occipital regions, including the cuneus, inferior occipital gyrus, and superior occipital gyrus, highlighting uniqueness-related visual-network information.
  • ROI importance: Important ROIs differ across datasets, indicating that IID-GCN captures disorder-specific information-channel patterns rather than relying on fixed brain regions.The analysis identifies dominant synergy channels for ADNI and PPMI, and uniqueness for ABIDE.
  • Latent subnetworks: Consensus matrices show distinct synergy-channel subnetwork organizations across CN, MCI, and AD, with diagnosis-dependent block-like patterns.These patterns suggest disease-stage-related changes in synergy-based functional information organization.
  • Interpretation: Across ADNI, PPMI, and ABIDE, interpretability analyses support complementary diagnostic information beyond traditional correlation-based functional connectivity.The findings suggest that disorders affect the organization of redundancy, uniqueness, and synergy as well as connectivity strength.
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