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Measuring Spatially- and Directionally-varying Light Scattering from Biological Material

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The Manifold Scattering Transform for High-Dimensional Point Cloud Data.

Joyce Chew¹, Holly R Steach², Siddharth Viswanath³

¹UCLA Department of Mathematics, Los Angeles, CA, USA.

Proceedings of Machine Learning Research

|May 9, 2023

Summary

This summary is machine-generated.

This study introduces practical methods for the manifold scattering transform, a deep learning tool for data on complex shapes. These new techniques enable effective signal and manifold classification in real-world datasets.

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Area of Science:

Machine Learning
Geometric Deep Learning
Data Science

Background:

The manifold scattering transform is a novel deep feature extractor for data residing on Riemannian manifolds.
Existing implementations are limited, primarily to 2D surfaces with predefined meshes, hindering broader application.
Theoretical focus on stability and invariance properties has overshadowed practical numerical implementation.

Purpose of the Study:

To present practical numerical implementation schemes for the manifold scattering transform.
To extend the applicability of the manifold scattering transform to high-dimensional point cloud data modeled on low-dimensional manifolds.
To demonstrate the effectiveness of these schemes for classification tasks in naturalistic systems.

Main Methods:

Development of practical implementation schemes for the manifold scattering transform.
Leveraging the theory of diffusion maps for numerical computation.
Application to datasets from naturalistic systems, specifically single-cell genetics data represented as point clouds.

Main Results:

Successful implementation of the manifold scattering transform for high-dimensional point cloud data.
Demonstrated effectiveness of the proposed methods for signal classification tasks.
Validated the utility of the methods for manifold classification tasks.

Conclusions:

The developed diffusion map-based schemes provide a practical approach to implementing the manifold scattering transform.
These methods significantly enhance the utility of the manifold scattering transform for analyzing complex, real-world datasets.
The approach is effective for classification tasks in fields like single-cell genetics.