Geometric Scattering on Measure Spaces
Joyce Chew, Matthew Hirn, Smita Krishnaswamy, Deanna Needell, and Michael Perlmutter, Holly Steach, Siddharth Viswanath, Hau-Tieng, Wu

TL;DR
This paper introduces a unified geometric scattering framework for measure spaces, extending previous models to more general data structures and providing methods for approximation and stability analysis, with applications to diverse data types.
Contribution
It presents a general model for geometric scattering on measure spaces, including new invariance criteria and data-driven approximation methods for complex data structures.
Findings
Unified geometric scattering model applicable to various data structures
Proposed invariance criterion ensures stability and invariance properties
Demonstrated effectiveness on spherical images, directed graphs, and single-cell data
Abstract
The scattering transform is a multilayered, wavelet-based transform initially introduced as a model of convolutional neural networks (CNNs) that has played a foundational role in our understanding of these networks' stability and invariance properties. Subsequently, there has been widespread interest in extending the success of CNNs to data sets with non-Euclidean structure, such as graphs and manifolds, leading to the emerging field of geometric deep learning. In order to improve our understanding of the architectures used in this new field, several papers have proposed generalizations of the scattering transform for non-Euclidean data structures such as undirected graphs and compact Riemannian manifolds without boundary. In this paper, we introduce a general, unified model for geometric scattering on measure spaces. Our proposed framework includes previous work on geometric…
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Taxonomy
TopicsRadiomics and Machine Learning in Medical Imaging · Advanced Graph Neural Networks · Medical Imaging and Analysis
