In this paper, we focus on the intersections of a manifold's local structures to analyze the global structure of a manifold. We obtain local regions on data manifolds such as the latent space of StyleGAN2, using Mapper, a tool from topological data analysis. We impose gluing compatibility conditions on overlapping local regions, which guarantee that the local structures can be glued together to the global structure of a manifold. We propose a novel generative flow model called Atlas flow that uses compatibility to reattach the local regions. Our model shows that the generating processes perform well on synthetic dataset samples of well-known manifolds with noise. Furthermore, we investigate the style vector manifold of StyleGAN2 using our model.
Cite
@article{arxiv.2210.14149,
title = {Atlas flow : compatible local structures on the manifold},
author = {Taejin Paik and Jaemin Park and Jung Ho Park},
journal= {arXiv preprint arXiv:2210.14149},
year = {2022}
}