2022/10/24 by Taejin Paik, Jaemin Park, Paik, Taejin +3 · 1 citation
Computer Science · Mathematics · #62R40 #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #I.2.10 #I.2.6 #Machine Learning (cs.LG) #Morphological variations and asymmetry #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2210.14149
openalex publication_date 2022/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.