Search Results for author: Stefan C. Schonsheck

Found 6 papers, 0 papers with code

Multiscale Hodge Scattering Networks for Data Analysis

no code implementations17 Nov 2023 Naoki Saito, Stefan C. Schonsheck, Eugene Shvarts

Our construction is based on multiscale basis dictionaries on simplicial complexes, i. e., the $\kappa$-GHWT and $\kappa$-HGLET, which we recently developed for simplices of dimension $\kappa \in \mathbb{N}$ in a given simplicial complex by generalizing the node-based Generalized Haar-Walsh Transform (GHWT) and Hierarchical Graph Laplacian Eigen Transform (HGLET).

Descriptive

Semi-Supervised Manifold Learning with Complexity Decoupled Chart Autoencoders

no code implementations22 Aug 2022 Stefan C. Schonsheck, Scott Mahan, Timo Klock, Alexander Cloninger, Rongjie Lai

Our numerical experiments on synthetic and real-world data verify that the proposed model can effectively manage data with multi-class nearby but disjoint manifolds of different classes, overlapping manifolds, and manifolds with non-trivial topology.

Representation Learning

Computational Analysis of Deformable Manifolds: from Geometric Modelling to Deep Learning

no code implementations3 Sep 2020 Stefan C. Schonsheck

More specifically, we will study techniques for representing manifolds and signals supported on them through a variety of mathematical tools including, but not limited to, computational differential geometry, variational PDE modeling, and deep learning.

Unsupervised Geometric Disentanglement for Surfaces via CFAN-VAE

no code implementations23 May 2020 N. Joseph Tatro, Stefan C. Schonsheck, Rongjie Lai

We also successfully detect a level of geometric disentanglement in mesh convolutional autoencoders that encode xyz-coordinates directly by registering its latent space to that of CFAN-VAE.

Disentanglement Pose Transfer

Nonisometric Surface Registration via Conformal Laplace-Beltrami Basis Pursuit

no code implementations19 Sep 2018 Stefan C. Schonsheck, Michael M. Bronstein, Rongjie Lai

In this paper, we propose a variational model to align the Laplace-Beltrami (LB) eigensytems of two non-isometric genus zero shapes via conformal deformations.

Parallel Transport Convolution: A New Tool for Convolutional Neural Networks on Manifolds

no code implementations21 May 2018 Stefan C. Schonsheck, Bin Dong, Rongjie Lai

PTC allows for the construction of compactly supported filters and is also robust to manifold deformations.

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