AI Article Synopsis
- The manifold scattering transform is a deep learning tool designed for analyzing data on Riemannian manifolds, extending concepts from convolutional neural networks to more complex geometries.
- Previous research primarily examined its theoretical aspects but lacked practical numerical methods, particularly outside of two-dimensional settings.
- This new work introduces diffusion map-based techniques for applying the transform to high-dimensional datasets, such as those found in single-cell genetics, demonstrating effectiveness in classifying signals and manifolds.
Article 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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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC10164360 | PMC |
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