mlsanityData to 14 Oct 2026

The Manifold Scattering Transform for High-Dimensional Point Cloud Data

arXiv 2206.10078 ↗First posted 21 Jun 2022cs.LG cs.NA eess.SPcited by 9

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Abstract (arXiv)

The manifold scattering transform is a deep feature extractor for data defined on a Riemannian manifold. It is one of the first examples of extending convolutional neural network-like operators to general manifolds. The initial work on this model focused primarily on its theoretical stability and invariance properties but did not provide methods for its numerical implementation except in the case of two-dimensional surfaces with predefined meshes. In this work, we present practical schemes, based on the theory of diffusion maps, for implementing the manifold scattering transform to datasets arising in naturalistic systems, such as single cell genetics, where the data is a high-dimensional point cloud modeled as lying on a low-dimensional manifold. We show that our methods are effective for signal classification and manifold classification tasks.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 27 of its 53 references that are in the map. First posted on arXiv 21 Jun 2022.

Builds on

27 of 53 references.

References · 27

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15 more
  1. 2018Geometric Scattering for Graph Data Analysiscited by 49
  2. 2018Graph Convolutional Neural Networks via Scatteringcited by 46
  3. 2018Diffusion Scattering Transforms on Graphscited by 44
  4. 2019Stability of Graph Scattering Transformscited by 34
  5. 2022Can Hybrid Geometric Scattering Networks Help Solve the Maximum Clique Problem?cited by 25
  6. 2021Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolationcited by 24
  7. 2020Spatio-Temporal Graph Scattering Transformcited by 19
  8. 2021Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNscited by 18
  9. 2021Diffusion Earth Mover's Distance and Distribution Embeddingscited by 18
  10. 2022Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networkscited by 18
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  12. 2021Stability of Neural Networks on Manifolds to Relative Perturbationscited by 9
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  15. 2018A CNN for homogneous Riemannian manifolds with applications to Neuroimagingcited by 1

Built on by

Cited by year

Citing papers per year: 2022: 2; 2023: 2; 2024: 2; 2025: 3.

9 papers.

  1. 2022Learnable Filters for Geometric Scattering Modulescited by 9
  2. 2022A Convergence Rate for Manifold Neural Networkscited by 6
  3. 2023Persistent Homology for High-dimensional Data Based on Spectral Methodscited by 3
  4. 2023Manifold Filter-Combine Networkscited by 2
  5. 2025HiPoNet: A Multi-View Simplicial Complex Network for High Dimensional Point-Cloud and Single-Cell Datacited by 2
  6. 2024Point Cloud Classification via Deep Set Linearized Optimal Transportcited by 1
  7. 2025VDW-GNNs: Vector diffusion wavelets for geometric graph neural networkscited by 1
  8. 2024Convergence of Manifold Filter-Combine Networkscited by 0
  9. 2025InfoGain Wavelets: Furthering the Design of Graph Diffusion Waveletscited by 0