BrainLinear: A Linear Model for Brain Network Analysis in Sparse Tangent Subspaces

Sijing Wu; Dongyuan Li; Miaoting Huang; Weiwei Ye; Ying Zhang; Feng Xia; Renhe Jiang

cs.GRAug 15, 2026

BrainLinear: A Linear Model for Brain Network Analysis in Sparse Tangent Subspaces

Authors: Sijing Wu, Dongyuan Li, Miaoting Huang, Weiwei Ye, Ying Zhang, Feng Xia, Renhe Jiang

Organizations: Guangdong University of Foreign Studies · The University of Tokyo · RIKEN AIP · Royal Melbourne Institute of Technology

Abstract

Functional connectome analysis examines brain-region interactions to understand and identify disorders such as autism spectrum disorder and Alzheimer's disease. Existing methods typically use GNNs and Transformers to model the full functional connectivity matrix. However, processing tens of thousands of connections introduces redundancy and noise, increases computational cost, and limits connection-level interpretability. This raises a central question: do we really need complex interaction modeling, or is identifying a small set of disease-relevant connectivity patterns sufficient? To answer this question, we propose BrainLinear, a lightweight geometry-aware framework for mining disease-discriminative connectome patterns. BrainLinear first maps each functional connectivity matrix to a shared tangent space centered at the Fréchet mean of the training set, capturing subject-specific deviations while respecting matrix geometry. It then scores each ROI-pair tangent direction by its classification contribution and disease--control difference, retaining Top- $K$ directions as a compact representation. Finally, a shallow multilayer perceptron performs classification on the selected representation. Experiments on ABIDE and ADNI show that BrainLinear matches or exceeds strong GNN and Transformer baselines at a fraction of their cost: it improves AUC and ACC over the best baseline for each metric by up to $3.54$ and $1.39$ percentage points, while reducing runtime and peak GPU memory by $84.0\%$ and $68.4\%$ relative to the closest baseline in AUC. The selected directions are directionally consistent with between-group displacements and organized across major functional systems, supporting connection-level interpretation.

Figures & tables

Figure 1: Overview of BrainLinear. Functional connectomes are mapped to a shared AIRM tangent space, where disease-discriminative ROI-pair coordinates are selected by joint probe relevance and group displacement for lightweight classification.

	Model	ABIDE				ADNI
	Model	AUC $\uparrow$	ACC $\uparrow$	SEN $\uparrow$	SPE $\uparrow$	AUC $\uparrow$	ACC $\uparrow$	SEN $\uparrow$	SPE $\uparrow$
GNN	BrainGNN	64.42 $\pm$ 3.57	63.09 $\pm$ 1.35	65.65 $\pm$ 2.88	60.67 $\pm$ 3.68	61.81 $\pm$ 1.58	58.72 $\pm$ 3.14	52.88 $\pm$ 9.70	62.70 $\pm$ 4.26
	BrainGB	70.32 $\pm$ 3.66	65.12 $\pm$ 3.90	67.01 $\pm$ 10.00	60.07 $\pm$ 8.53	66.44 $\pm$ 3.33	63.70 $\pm$ 4.65	60.73 $\pm$ 8.25	64.67 $\pm$ 9.07
	FBNetGen	74.50 $\pm$ 3.77	67.09 $\pm$ 3.37	64.71 $\pm$ 9.85	69.61 $\pm$ 9.30	67.05 $\pm$ 2.16	63.26 $\pm$ 1.38	66.79 $\pm$ 6.93	61.31 $\pm$ 9.65
	GCN	59.59 $\pm$ 3.44	59.30 $\pm$ 3.38	56.67 $\pm$ 4.37	61.55 $\pm$ 5.29	62.45 $\pm$ 3.63	59.12 $\pm$ 4.53	54.55 $\pm$ 9.96	62.00 $\pm$ 8.55
	GAT	60.43 $\pm$ 3.88	60.10 $\pm$ 4.13	59.26 $\pm$ 5.51	62.89 $\pm$ 8.03	62.00 $\pm$ 2.88	58.75 $\pm$ 2.86	53.20 $\pm$ 7.50	64.79 $\pm$ 7.65

Table 1: Classification performance comparison. Best results are in bold with shaded cells; second best are underlined .

Variant	ABIDE				ADNI
Variant	AUC $\uparrow$	ACC $\uparrow$	SEN $\uparrow$	SPE $\uparrow$	AUC $\uparrow$	ACC $\uparrow$	SEN $\uparrow$	SPE $\uparrow$
Raw FC + MLP	65.41 $\pm$ 3.15	60.80 $\pm$ 2.13	58.66 $\pm$ 5.63	62.00 $\pm$ 7.60	67.47 $\pm$ 13.88	58.33 $\pm$ 12.84	63.33 $\pm$ 35.17	56.38 $\pm$ 16.21
Full Tangent + MLP	77.30 $\pm$ 1.31	67.62 $\pm$ 2.49	82.45 $\pm$ 3.41	53.65 $\pm$ 7.43	70.61 $\pm$ 3.78	64.75 $\pm$ 3.16	62.42 $\pm$ 6.27	67.03 $\pm$ 11.05
Random- $K$ Tangent + MLP	72.06 $\pm$ 1.83	63.66 $\pm$ 1.24	74.08 $\pm$ 7.99	53.85 $\pm$ 9.81	65.29 $\pm$ 4.64	60.50 $\pm$ 4.99	60.94 $\pm$ 10.75	60.01 $\pm$ 13.87
Coefficient-only Top- $K$	76.48 $\pm$ 1.13	67.92 $\pm$ 3.63	73.27 $\pm$ 10.29	62.88 $\pm$ 16.00	70.41 $\pm$ 3.75	64.36 $\pm$ 3.96	72.37 $\pm$ 8.66	56.80 $\pm$ 13.53
Displacement-only Top- $K$	77.68 $\pm$ 0.83	68.61 $\pm$ 1.74	79.80 $\pm$ 2.54	58.08 $\pm$ 5.29	70.68 $\pm$ 4.41	64.75 $\pm$ 2.70	69.71 $\pm$ 15.58	60.05 $\pm$ 14.69

Table 2: Ablation results on ABIDE and ADNI (%). Best results are in bold with shaded cells; second best are underlined .

Figure 2: Performance-efficiency comparison on ABIDE.

Panel of Figure 3 — Figure 3: Sensitivity analysis under different sparsity budgets.

Panel of Figure 4 — Figure 4: Discriminative relevance across tangent coordinates.

Panel of Figure 5 — Figure 5: Validation of selected tangent directions on ABIDE.

Panel of Figure 6 — Figure 6: Biological interpretation of tangent directions.

Panel of Figure 7 — Figure 7: Brain-space distribution of tangent directions.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Feature	Classifier	ABIDE				ADNI
Feature	Classifier	AUC $\uparrow$	ACC $\uparrow$	SEN $\uparrow$	SPE $\uparrow$	AUC $\uparrow$	ACC $\uparrow$	SEN $\uparrow$	SPE $\uparrow$
Raw FC	Logistic	65.41	60.80	58.66	62.00	66.14	60.83	51.56	66.76
	SVM	68.57	62.34	52.35	71.90	62.38	57.50	59.56	55.62
	MLP	69.17 $\pm$ 4.11	63.93 $\pm$ 2.31	54.37 $\pm$ 10.22	73.06 $\pm$ 7.90	67.97 $\pm$ 6.49	59.17 $\pm$ 8.25	63.33 $\pm$ 19.85	55.90 $\pm$ 23.15
Full Tangent	Logistic	73.34	66.20	56.38	75.58	67.47	58.33	63.33	56.38
	SVM	73.21	66.60	58.41	74.41	68.28	59.17	43.11	70.29

Appendix

Table 3: Effect of classifier choice on different feature representations. Best results are highlighted in bold with shaded cells.

Rank	ROI Pair	Network Pair	$\Delta_{e}$	$\alpha_{e}$	Importance	Direction
1	Precentral_L–Occipital_Mid_L	Somatomotor–Unassigned	0.0405	0.3167	0.0128	Positive
2	Hippocampus_R–Frontal_Sup_L	Frontoparietal–DefaultMode	-0.0343	-0.3740	0.0128	Negative
3	Caudate_L–Caudate_R	Somatomotor–Limbic	-0.0514	-0.2431	0.0125	Negative
4	Frontal_Mid_L–Temporal_Mid_L	Frontoparietal–Visual	-0.0431	-0.2761	0.0119	Negative
5	Cerebelum_Crus1_R–Lingual_L	Unassigned–Limbic	0.0355	0.3331	0.0118	Positive
6	Frontal_Med_Orb_L–Precuneus_L	Somatomotor–Visual	-0.0376	-0.3073	0.0115	Negative

Appendix

Table 4: Top-ranked discriminative tangent directions identified by BrainLinear. The importance score is defined as

s_{e}=|\alpha_{e}\Delta_{e}|

Pattern	Directions	Importance
$\Delta>0,\alpha>0$	4089	7.2430
$\Delta<0,\alpha<0$	3905	6.9698
$\Delta>0,\alpha<0$	4	0.0024
$\Delta<0,\alpha>0$	2	0.0013

Appendix

Table 5: Sign consistency analysis of selected discriminative tangent directions.

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