HiPoNet: A Topology-Preserving Multi-View Neural Network For High Dimensional Point Cloud and Single-Cell Data

2025-02-11

AI Summary

Preserving higher-order topological structures in high-dimensional point clouds—such as single-cell and spatial transcriptomics data—remains challenging, especially for scalable learning across large cohorts. Method: We propose the first end-to-end differentiable simplicial complex learning framework: it constructs multi-view simplicial complexes via learnable feature reweighting and integrates simplex-based wavelet transforms to enable multi-scale topological representation learning. Contribution/Results: Our method explicitly models and preserves high-order topology—novel in single-cell analysis—and unifies learnable complex construction, multi-view feature fusion, and differentiable neural architecture design. Experiments demonstrate significant improvements over state-of-the-art point cloud and graph models on single-cell classification and regression tasks. Moreover, the framework generalizes effectively to spatial transcriptomics data, validating its cross-modal robustness and scalability to million-cell-scale datasets.

Technology Category

• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Security and Privacy: Data transparency and provenance

Abstract

In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Single-cell data can have high dimensionality exceeding the capabilities of existing methods point cloud tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e. one on 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 information. In contrast, HiPoNet forms higher-order simplicial complexes through learnable feature reweighting, generating multiple data views that disentangle distinct biological processes. It then employs simplicial wavelet transforms to extract multi-scale features - capturing both local and global topology. We empirically show that these components preserve topological information in the learned representations, and that HiPoNet significantly outperforms state-of-the-art point-cloud and graph-based models on single cell. We also show an application of HiPoNet on spatial transcriptomics datasets using spatial co-ordinates as one of the views. Overall, HiPoNet offers a robust and scalable solution for high-dimensional data analysis.

Problem

• High-dimensional point cloud analysis
• Single-cell data processing
• Topology-preserving neural network

Innovation

• End-to-end differentiable neural network
• Higher-order simplicial complexes
• Simplicial wavelet transforms