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HiPoNet: A Multi-View Simplicial Complex Network for High Dimensional Point-Cloud and Single-Cell data
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Proposes HiPoNet, an end-to-end differentiable network that learns multiple feature-reweighted views of high-dimensional point clouds, builds Vietoris-Rips simplicial complexes per view, and aggregates simplicial wavelet scattering coefficients for point-cloud-level classification and regression.
Problem
Point-cloud-level classification and regression on high-dimensional point clouds (e.g., single-cell cohorts with many patients and tens of features), where existing point cloud and graph neural networks are designed for 3D data and single kNN graphs discard geometric and topological structure.
Approach
Learn several feature-reweighting vectors to produce multiple views, build a differentiable Vietoris-Rips simplicial complex per view, and extract multiscale features with simplicial diffusion wavelets and scattering coefficients rather than message passing, giving theoretical links to 0-homology and geodesic distance.
Key results
- On Melanoma classification HiPoNet reaches 90.90 ± 4.92 accuracy vs 88.18 for TopoGNN and 85.45 for KNN-GIN; on PDO it reaches 77.38 ± 0.94, second to TopoGNN's 79.90 ± 16.15.
- On persistence feature prediction HiPoNet achieves MSE 0.633 on Melanoma and 0.4046 on PDO, lower than all KNN-GNN and point-cloud baselines.
- On CODEX spatial data HiPoNet has the best AUC on DFCI (0.916), Charville outcome/recurrence (0.681/0.681) and Melanoma (0.732).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use HiPoNet instead of KNN-SAGE for persistence prediction | Persistence prediction · Melanoma | MSE: 0.734 $\pm$ 0.031 -> 0.633 $\pm$ 0.043 | Helped |
| Use HiPoNet instead of KNN-GAT for persistence prediction | Persistence prediction · PDO | MSE: 1.068 $\pm$ 0.008 -> 0.4046 $\pm$ 0.006 | Helped |
| Use HiPoNet instead of the strongest reported baseline | Single-cell classification · Melanoma | accuracy: 88.18 $\pm$ 8.19 -> 90.90 $\pm$ 4.92 | Helped |
| Use HiPoNet instead of the strongest reported baseline | Single-cell classification · PDO | accuracy: 79.90 $\pm$ 16.15 -> 77.38 $\pm$ 0.94 | Hurt |
| Use HiPoNet instead of the strongest reported baseline | Spatial transcriptomics classification · DFCI outcome | AUC-ROC: 0.82 $\pm$ 0.040 -> 0.916 $\pm$ 0.03 | Helped |
| Use HiPoNet instead of the strongest reported baseline | Spatial transcriptomics classification · Charville outcome | AUC-ROC: 0.675 $\pm$ 0.051 -> 0.681 $\pm$ 0.012 | Helped |
| Use HiPoNet instead of the strongest reported baseline | Spatial transcriptomics classification · Charville recurrence | AUC-ROC: 0.642 $\pm$ 0.056 -> 0.681 $\pm$ 0.01 | Helped |
| Use HiPoNet instead of the strongest reported baseline | Spatial transcriptomics classification · UPMC outcome | AUC-ROC: 0.668 $\pm$ 0.032 -> 0.665 $\pm$ 0.01 | Hurt |
| Use HiPoNet instead of the strongest reported baseline | Spatial transcriptomics classification · UPMC recurrence | AUC-ROC: 0.514 $\pm$ 0.02 -> 0.6044 $\pm$ 0.0 | Helped |
| Use HiPoNet instead of the strongest reported baseline | Spatial transcriptomics classification · Melanoma response | AUC-ROC: 0.606 $\pm$ 0.13 -> 0.732 $\pm$ 0.01 | Helped |
| Increase the number of views from 1 to 4 (ablation) | HiPoNet · Melanoma classification | accuracy: 27.27 $\pm$ 12.85 -> 90.90 $\pm$ 4.92 | Helped |
| Increase the number of views from 1 to 4 (ablation) | HiPoNet · PDO classification | accuracy: 59.80 $\pm$ 1.99 -> 77.38 $\pm$ 0.94 | Helped |
Surprising findings
- Point-cloud models designed for 3D (DGCNN, PointNet++, PointTransformer) have very large MSE on persistence prediction, e.g. about 28 on Melanoma and 1353 for DGCNN on PDO.
- Higher-order simplices (K=2,3) do not uniformly help; K=1 (graph-like) is best for PDO while K=2 helps some Charville outcome predictions.
Limitations
- Vietoris-Rips threshold and kernel bandwidth are sensitive hyperparameters; optimal values vary across datasets.
- Results rely on a small number of seeds (5) and high variance on some tasks, e.g. TopoGNN and HiPoNet on Melanoma.
- Theoretical results (0-homology, geodesic distance, curvature) rely on manifold assumptions and proof sketches in the main text.
Experimental setup
Datasets: Melanoma MIBI cohort Patient-derived organoids (PDO) cohort CODEX spatial transcriptomics cohorts (DFCI, Charville, UPMC)
Benchmarks: Melanoma MIBI classification PDO classification Persistence feature prediction (Melanoma, PDO) CODEX spatial transcriptomics outcome/recurrence prediction
Metrics: accuracy MSE AUC ROC
Baselines: KNN-GCN KNN-SAGE KNN-GAT KNN-GIN KNN-GraphTransformer TopoGNN PointNet++ DGCNN PointTransformer TopoAE GCNN HGCNN
Builds on: geometric scattering transform diffusion wavelets PointNet++ DGCNN simplicial neural networks
Closest papers by meaning
- SPLATNet: Sparse Lattice Networks for Point Cloud Processing (CVPR 2018 · similarity 0.84)
- Towards Scalable Context-Aware Single-Cell Spatial Transcriptomics Prediction from Histology Images (NeurIPS 2026 · similarity 0.83)
- Global Context-aware Representation Learning for Spatially Resolved Transcriptomics (ICML 2025 · similarity 0.83)
- MERGE: Multi-faceted Hierarchical Graph-based GNN for Gene Expression Prediction from Whole Slide Histopathology Images (CVPR 2025 · similarity 0.83)
- Multi-modal Topology-embedded Graph Learning for Spatially Resolved Genes Prediction from Pathology Images with Prior Gene Similarity Information (CVPR 2025 · similarity 0.82)
- DeepLA-Net: Very Deep Local Aggregation Networks for Point Cloud Analysis (CVPR 2025 · similarity 0.82)
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