# HiPoNet: A Multi-View Simplicial Complex Network for High Dimensional Point-Cloud and Single-Cell Data

arXiv: https://arxiv.org/abs/2502.07746 · HTML: https://mlsanity.com/paper/2502.07746/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 64 references that are in the map.
- First posted on arXiv 11 Feb 2025.

## Builds on (most cited first, 30 of 35)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Rethinking Network Design and Local Geometry in Point Cloud: A Simple Residual MLP Framework](https://mlsanity.com/paper/2202.07123/) (2022)
- [A Note on Over-Smoothing for Graph Neural Networks](https://mlsanity.com/paper/2006.13318/) (2020)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [Topological Signal Processing over Simplicial Complexes](https://mlsanity.com/paper/1907.11577/) (2019)
- [Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplacian](https://mlsanity.com/paper/1807.05044/) (2018)
- [Blessing of dimensionality: mathematical foundations of the statistical physics of data](https://mlsanity.com/paper/1801.03421/) (2018)
- [Geometric Scattering for Graph Data Analysis](https://mlsanity.com/paper/1810.03068/) (2018)
- [Graph Convolutional Neural Networks via Scattering](https://mlsanity.com/paper/1804.00099/) (2018)
- [Diffusion Scattering Transforms on Graphs](https://mlsanity.com/paper/1806.08829/) (2018)
- [Stability of Graph Scattering Transforms](https://mlsanity.com/paper/1906.04784/) (2019)
- [Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networks](https://mlsanity.com/paper/2201.08932/) (2022)
- [TopoTune : A Framework for Generalized Combinatorial Complex Neural Networks](https://mlsanity.com/paper/2410.06530/) (2024)
- [Understanding Graph Neural Networks with Generalized Geometric Scattering Transforms](https://mlsanity.com/paper/1911.06253/) (2019)
- [The Manifold Scattering Transform for High-Dimensional Point Cloud Data](https://mlsanity.com/paper/2206.10078/) (2022)
- [Learnable Filters for Geometric Scattering Modules](https://mlsanity.com/paper/2208.07458/) (2022)
- [Diffusion Curvature for Estimating Local Curvature in High Dimensional Data](https://mlsanity.com/paper/2206.03977/) (2022)
- [A Heat Diffusion Perspective on Geodesic Preserving Dimensionality Reduction](https://mlsanity.com/paper/2305.19043/) (2023)

## Built on by (most cited first, 2 of 2)

- [VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks](https://mlsanity.com/paper/2510.01022/) (2025)
- [Neural Point-Forms](https://mlsanity.com/paper/2605.15524/) (2026)

## Abstract (arXiv)

In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Our work is motivated by single-cell data which can have very high-dimensionality --exceeding the capabilities of existing methods for point clouds which are mostly tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e., one data set for every patient), necessitating models that can process large, high-dimensional point-clouds at scale. Most current approaches build a single nearest-neighbor graph, discarding important geometric and topological information. In contrast, HiPoNet models the point-cloud as a set of higher-order simplicial complexes, with each particular complex being created using a reweighting of features. This method thus generates multiple constructs corresponding to different views of high-dimensional data, which in biology offers the possibility of disentangling distinct cellular processes. It then employs simplicial wavelet transforms to extract multiscale features, capturing both local and global topology from each view. We show that geometric and topological information is preserved in this framework both theoretically and empirically. We showcase the utility of HiPoNet on point-cloud level tasks, involving classification and regression of entire point-clouds in data cohorts. Experimentally, we find that HiPoNet outperforms other point-cloud and graph-based models on single-cell data. We also apply HiPoNet to spatial transcriptomics datasets using spatial coordinates as one of the views. Overall, HiPoNet offers a robust and scalable solution for high-dimensional data analysis.