  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.
