HOI-Brain: a novel multi-channel transformers framework for brain disorder diagnosis by accurately extracting signed higher-order interactions from fMRI

Abstract

Accurately characterizing higher-order interactions of brain regions and extracting interpretable organizational patterns from Functional Magnetic Resonance Imaging data is crucial for brain disease diagnosis. Current graph-based deep learning models primarily focus on pairwise or triadic patterns while neglecting signed higher-order interactions, limiting comprehensive understanding of brain-wide communication. We propose HOI-Brain, a novel computational framework leveraging signed higher-order interactions and organizational patterns in fMRI data for brain disease diagnosis. First, we introduce a co-fluctuation measure based on Multiplication of Temporal Derivatives to detect higher-order interactions with temporal resolution. We then distinguish positive and negative synergistic interactions, encoding them in signed weighted simplicial complexes to reveal brain communication insights. Using Persistent Homology theory, we apply two filtration processes to these complexes to extract signed higher-dimensional neural organizations spatiotemporally. Finally, we propose a multi-channel brain Transformer to integrate heterogeneous topological features. Experiments on Alzheimer' s disease, Parkinson' s syndrome, and autism spectrum disorder datasets demonstrate our framework' s superiority, effectiveness, and interpretability. The identified key brain regions and higher-order patterns align with neuroscience literature, providing meaningful biological insights.

Figures (11)

• Figure 1: Overall framework of HOI-Brain. Individual fMRI data are transformed into $N$ original fMRI signals through a preprocessing pipeline. A novel metric - Multiplication of Temporal Derivatives (MTD) - is used to quantify dynamic functional co-fluctuations of group ROIs. Then, at each timepoint t, some instantaneous k-order co-fluctuations are encoded into four signed monotonic weighted simplicial complexes based on filtrations, respectively. Persistent Homology is applied to analyze these signed monotonic weighted simplicial complexes at each t. Five feature matrices are generated by extracting all edges, signed good quadruplets, and signed 2D voids. These matrices are temporally averaged across all timepoints to stabilize feature representations. By incorporating the lower-order and higher-order features, a multi-channel brain network Transformer is used to produce the final classification of the disease status (e.g., Classes 1, 2 and 3 correspond to CN, MCI and AD in ADNI).
• Figure 2: (a) illustrates two examples of monotonic weighted simplicial complexes (left) that satisfy the lower-closure condition and one example (right) that satisfies the upper-closure condition. The red numbers denote the weights of 1-simplices, and the text below indicates the weights of 2-simplices and 3-simplices. (b) illustrates six types of signed quadruplet higher-order interactions. For example, positively synergistic quadruplet interactions indicate that the activation values of the four brain regions increase simultaneously at time t relative to time t-1. We focus exclusively on the first two interaction types with concordant positive signs (all non-negative or all non-positive). (c) illustrates the construction of the feature matrices: 2D-void features are encoded from the homological scaffold, whereas quadruplet signatures are encoded by projecting signed quadruplets onto edges to obtain edge-based matrices that retain higher-order interaction information. (d) illustrates a single-channel, single-head self-attention layer, where the input node feature matrix is linearly projected into queries, keys, and values, and the output is obtained by aggregating value vectors weighted by the scaled dot-product attention.
• Figure 3: (a), (b), (d), and (e) present the ablation study of the multi-channel brain network Transformer in HOI-Brain across all datasets, comparing the full model with three degenerated variants: wo-signed (removing the signed higher-order feature decoupling mechanism), wo-fusion (removing the attention-guided feature fusion mechanism), and wo-cluster (removing the orthonormal clustering readout across multiple channels). (c) and (f) examine the impact of a key hyperparameter, the number of clusters K, on model performance, reported in terms of accuracy and recall, respectively. The results show that the model’s performance improves as the number of clusters K increases from 2 to 10 or 20 but declines when K rises from 10 or 20 to 100.
• Figure 4: (a) and (b) show, for the ADNI and ABIDE datasets respectively, the distributions of the learned weights for the three channels (left), the distributions of the learned signed weights for the quadruplet channel (middle), and the distributions of the learned signed weights for the void channel (right). (c) presents the group-difference analysis on ADNI using Mann–Whitney U tests. Violin plots (with embedded box summaries) depict the average counts of positive/negative signed quadruplet interaction signatures and positive/negative signed two-dimensional void descriptors across the CN, MCI, and AD groups. Pairwise significance after FDR correction is denoted as: $^{***}p<0.001$, $^{**}p<0.01$, $^{*}p<0.05$, and ns $p\ge 0.05$. (d) and (e) show, for the ADNI and ABIDE datasets, the attention patterns from the first layer of the multi-head self-attention module for the three channels (edge, quadruplet, and void), together with the corresponding cluster-assignment matrices produced by the multi-channel clustering readout.
• Figure 5: (a) shows the visualization of top 10 important brain regions (left) and top 10 important interactions between brain regions (right) associated with ADNI. The following two lines display the colors of the brain regions and their corresponding names. (b) shows the visualization of top 10 important brain regions (left) and top 10 important interactions of brain regions (right) associated with PPMI. (c) shows the visualization of top 10 important brain regions (left) and top 10 important interactions of brain regions (right) associated with ABIDE.

Theorems & Definitions (8)

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