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. 2022 Jul:196:67-78.

The Manifold Scattering Transform for High-Dimensional Point Cloud Data

Joyce Chew  1 , Holly R Steach  2 , Siddharth Viswanath  3 , Hau-Tieng Wu  4   5 , Matthew Hirn  6   7 , Deanna Needell  1 , Smita Krishnaswamy  2   8   9 , Michael Perlmutter  1
Affiliations

The Manifold Scattering Transform for High-Dimensional Point Cloud Data

Joyce Chew et al. Proc Mach Learn Res. 2022 Jul.

Abstract

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.

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Figures

Figure 1.
Figure 1.
The MNIST dataset projected onto the sphere.
Figure 2.
Figure 2.
Wavelets on the FAUST dataset, j = 1, 3, 5 from left to right. Positive values are red, while negative values are blue.
See this image and copyright information in PMC

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