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Haonan (Eric) Gao

NeurIPS 2026 Poster

Orthogonal Sparse Subgraph Alignment for Structure-Function Coupling in Brain Networks

Haonan Gao1 Daeyoung Ham2 Yifei Zhang1 Xinyuan Tian1 Shengxian Ding1 Yize Zhao1,† Tianxi Li3,†

1 Department of Biostatistics, Yale School of Public Health, Yale University

2 Department of Statistics and Data Science, University of Texas at San Antonio

3 School of Statistics, University of Minnesota, Twin Cities

† Corresponding authors: Yize Zhao and Tianxi Li

Publication Paper PDF BibTeX

At a glance. OSSA finds small sets of brain regions whose anatomical wiring aligns with how those regions function together. In the ABCD Study, it improved alignment on held-out participants compared with size-matched baselines, and the selected regions were consistent at the two-year follow-up.

Abstract

Characterizing the relationship between brain anatomical wiring and functional coordination remains a fundamental challenge in computational neuroscience. This difficulty primarily arises because structure-function coupling in the human brain is spatially heterogeneous, often localized to subnetworks, and inherently difficult to align across disparate representational modalities.

To address this methodological gap, we introduce Orthogonal Sparse Subgraph Alignment (OSSA), a principled and interpretable framework designed to identify compact structural cliques that exhibit maximal concordance with functional connectivity (FC) across subjects. Within each FC-derived community, OSSA optimizes an alignment objective over an orthogonal transformation, which absorbs coordinate mismatch between the two connectivity modalities, and a sparse node-selection vector, which identifies the induced structural connectivity (SC) subgraph.

Furthermore, for canonical OSSA within a fixed population community, we establish local statistical guarantees under the required assumptions. With high probability, an empirical local maximizer exists in a specified neighborhood of the population target, and every local maximizer in that neighborhood exactly recovers the active support and satisfies a nonasymptotic error bound for the aligned functional projector.

Extensive empirical evaluations on simulated data, alongside analyses of the Adolescent Brain Cognitive Development (ABCD) baseline and longitudinal cohorts, demonstrate that OSSA successfully recovers aligned structural cliques under latent cross-modal rotations. Ultimately, the proposed methodology significantly improves out-of-sample SC–FC alignment over size-matched baselines and identifies compact structural supports with longitudinal consistency in node selection, while multi-support diagnostics suggest a dominant aligned core within the estimated FC communities.

How OSSA works

OSSA extends orthogonal Procrustes alignment to a setting where the target subgraph is unknown. It identifies functional communities from training data, then learns an orthogonal transformation and selects a small set of structural nodes jointly within each community.

Three-stage OSSA pipeline: identify functional communities, jointly optimize orthogonal alignment and sparse node weights, then recover the induced structural subgraphs.
OSSA workflow. The learned node weights are rounded to select the nodes of each induced structural subgraph. The extension for multiple supports penalizes overlap and lets us assess whether a community contains more than one aligned core.

Results on the ABCD Study

OSSA improved structure–function alignment on held-out participants compared with size-matched baselines. At the two-year follow-up, the selected subnetworks shared an average of 2.86 of 3 nodes with the baseline selections.

Baseline cohort
2,350 subjects after QC
Year-2 cohort
1,897 subjects after QC
Canonical support
3 nodes per FC community
ABCD results: cortical maps of selection frequency in three FC communities, held-out alignment for five methods, positive null-corrected gains across sparsity budgets, and multiple supports separating only under large overlap penalties.
ABCD localization and diagnostics. (A) Selection frequency across split seeds at κ = 3; labels denote consensus supports. (B) Held-out rotation-aware alignment, mean ± s.e., for the five methods shown. (C) OSSA maintains positive SC-degree-quartile-matched gain across the tested budgets. (D) Multiple supports collapse at small λ and separate only under large penalties. View full-size figure
Evaluation details and baseline comparison

Improved held-out alignment

The analysis uses the 68-region Desikan–Killiany atlas and 60%, 20%, and 20% training, validation, and test splits across ten seeds. OSSA is compared with fourteen size-matched baselines and an ablation that fixes the rotation to the identity. Each baseline support is evaluated with its own rotation fitted on training data.

Selected baseline-cohort results at κ = 3.
Held-out alignment M1,aln, mean ± s.e. across 30 seed–community units.
MethodHeld-out alignment
OSSA10.55 ± 0.85
NMF9.96 ± 0.82
Sparse PLS9.22 ± 1.10
OSSA-noW3.82 ± 0.42

Comparisons across repeated splits are descriptive: the splits reuse subjects from the same cohort. Complete baseline results and evaluation details are in the paper.

Longitudinal support stability

The same protocol at Year 2 yields a cross-visit support replication score of 0.928 ± 0.033, based on support-set Jaccard overlap, with a mean overlap of 2.86 of 3 nodes.

A dominant aligned core

The multi-support diagnostic suggests a dominant aligned core within the estimated FC communities: additional supports collapse at small penalties, while forcing them apart lowers the primary held-out alignment objective.

The selected regions depend on the functional-community construction, sparsity budget, atlas, and cohort. Longitudinal support stability alone does not establish biological specificity.

Reference

Cite this work

Download .bib 
@inproceedings{gao2026orthogonal,
  title = {Orthogonal Sparse Subgraph Alignment for
           Structure-Function Coupling in Brain Networks},
  author = {Gao, Haonan and Ham, Daeyoung and Zhang, Yifei and
            Tian, Xinyuan and Ding, Shengxian and Zhao, Yize and
            Li, Tianxi},
  booktitle = {40th Conference on Neural Information
               Processing Systems (NeurIPS 2026)},
  year = {2026},
  url = {https://rampageoppa.github.io/projects/ossa/}
}