The Manifold Scattering Transform for High-Dimensional Point Cloud Data

Joyce Chew, Holly Steach, Siddharth Viswanath, Hau-Tieng Wu, Matthew Hirn, Deanna Needell, Matthew D. Vesely, Smita Krishnaswamy, Michael Perlmutter
Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022, PMLR 196:67-78, 2022.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v196-chew22a, title = {The Manifold Scattering Transform for High-Dimensional Point Cloud Data}, author = {Chew, Joyce and Steach, Holly and Viswanath, Siddharth and Wu, Hau-Tieng and Hirn, Matthew and Needell, Deanna and Vesely, Matthew D. and Krishnaswamy, Smita and Perlmutter, Michael}, booktitle = {Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022}, pages = {67--78}, year = {2022}, editor = {Cloninger, Alexander and Doster, Timothy and Emerson, Tegan and Kaul, Manohar and Ktena, Ira and Kvinge, Henry and Miolane, Nina and Rieck, Bastian and Tymochko, Sarah and Wolf, Guy}, volume = {196}, series = {Proceedings of Machine Learning Research}, month = {25 Feb--22 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v196/chew22a/chew22a.pdf}, url = {https://proceedings.mlr.press/v196/chew22a.html}, 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.} }
Endnote
%0 Conference Paper %T The Manifold Scattering Transform for High-Dimensional Point Cloud Data %A Joyce Chew %A Holly Steach %A Siddharth Viswanath %A Hau-Tieng Wu %A Matthew Hirn %A Deanna Needell %A Matthew D. Vesely %A Smita Krishnaswamy %A Michael Perlmutter %B Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022 %C Proceedings of Machine Learning Research %D 2022 %E Alexander Cloninger %E Timothy Doster %E Tegan Emerson %E Manohar Kaul %E Ira Ktena %E Henry Kvinge %E Nina Miolane %E Bastian Rieck %E Sarah Tymochko %E Guy Wolf %F pmlr-v196-chew22a %I PMLR %P 67--78 %U https://proceedings.mlr.press/v196/chew22a.html %V 196 %X 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.
APA
Chew, J., Steach, H., Viswanath, S., Wu, H., Hirn, M., Needell, D., Vesely, M.D., Krishnaswamy, S. & Perlmutter, M.. (2022). The Manifold Scattering Transform for High-Dimensional Point Cloud Data. Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022, in Proceedings of Machine Learning Research 196:67-78 Available from https://proceedings.mlr.press/v196/chew22a.html.

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