17 citations · 40 across the 8 of their papers we have counts for
9 papers
Multiscale Hodge Scattering Networks for Data Analysis
Naoki Saito, Stefan C. Schonsheck, Eugene Shvarts
We propose new scattering networks for signals measured on simplicial complexes, which we call \emph{Multiscale Hodge Scattering Networks} (MHSNs). Our construction builds on multi…
Multiscale Transforms for Signals on Simplicial Complexes
Naoki Saito, Stefan C. Schonsheck, Eugene Shvarts
Our previous multiscale graph basis dictionaries/graph signal transforms -- Generalized Haar-Walsh Transform (GHWT); Hierarchical Graph Laplacian Eigen Transform (HGLET); Natural G…
Spherical Coordinates from Persistent Cohomology
Nikolas C. Schonsheck, Stefan C. Schonsheck
We describe a method to obtain spherical parameterizations of arbitrary data through the use of persistent cohomology and variational optimization. We begin by computing the second…
Semi-Supervised Manifold Learning with Complexity Decoupled Chart Autoencoders
Stefan C. Schonsheck, Scott Mahan, Timo Klock +2
Autoencoding is a popular method in representation learning. Conventional autoencoders employ symmetric encoding-decoding procedures and a simple Euclidean latent space to detect h…
Computational Analysis of Deformable Manifolds: from Geometric Modelling to Deep Learning
Stefan C Schonsheck
Leo Tolstoy opened his monumental novel Anna Karenina with the now famous words: Happy families are all alike; every unhappy family is unhappy in its own way A similar notion also…
Unsupervised Geometric Disentanglement for Surfaces via CFAN-VAE
N. Joseph Tatro, Stefan C. Schonsheck, Rongjie Lai
Geometric disentanglement, the separation of latent codes for intrinsic (i.e. identity) and extrinsic(i.e. pose) geometry, is a prominent task for generative models of non-Euclidea…
Chart Auto-Encoders for Manifold Structured Data
Stefan Schonsheck, Jie Chen, Rongjie Lai
Deep generative models have made tremendous advances in image and signal representation learning and generation. These models employ the full Euclidean space or a bounded subset as…
Nonisometric Surface Registration via Conformal Laplace-Beltrami Basis Pursuit
Stefan C. Schonsheck, Michael M. Bronstein, Rongjie Lai
Surface registration is one of the most fundamental problems in geometry processing. Many approaches have been developed to tackle this problem in cases where the surfaces are near…
Parallel Transport Convolution: A New Tool for Convolutional Neural Networks on Manifolds
Stefan C. Schonsheck, Bin Dong, Rongjie Lai
Convolution has been playing a prominent role in various applications in science and engineering for many years. It is the most important operation in convolutional neural networks…