MFCGAN¶
Overview¶
This project pioneers a novel approach using neural networks within the generative adversarial network (GAN) framework for manifold fitting, a crucial challenge in non-linear data analysis. This method learns mappings between low-dimensional latent spaces and high-dimensional ambient spaces, akin to Riemannian exponential and logarithmic maps, providing manifold estimations, data projection, and even data generation within the manifold.
Through extensive simulations and real-data experiments, we demonstrate the precision and computational efficiency of our approach in capturing the underlying manifold's structure. This advancement holds significant potential in fields like statistics and computer science, offering control over manifold dimensionality and smoothness while enhancing data analysis. By integrating powerful neural network architectures with generative adversarial techniques, our research unlocks new possibilities for manifold fitting, spanning applications from dimensionality reduction and data visualization to authentic data generation, paving the way for future advancements in non-linear data analysis and inspiring further scholarly exploration.
Through extensive simulations and real-data experiments, we demonstrate the precision and computational efficiency of our approach in capturing the underlying manifold's structure. This advancement holds significant potential in fields like statistics and computer science, offering control over manifold dimensionality and smoothness while enhancing data analysis. By integrating powerful neural network architectures with generative adversarial techniques, our research unlocks new possibilities for manifold fitting, spanning applications from dimensionality reduction and data visualization to authentic data generation, paving the way for future advancements in non-linear data analysis and inspiring further scholarly exploration.
An implementation in Pytorch is available on Github:
Detailed description and discussion can be found in paper:
To cite:
@article{doi:10.1073/pnas.2311436121,
author = {Zhigang Yao and Jiaji Su and Shing-Tung Yau },
title = {Manifold fitting with CycleGAN},
journal = {Proceedings of the National Academy of Sciences},
volume = {121},
number = {5},
pages = {e2311436121},
year = {2024},
doi = {10.1073/pnas.2311436121},
URL = {https://www.pnas.org/doi/abs/10.1073/pnas.2311436121}
}
Selected Talks¶
Tsinghua Seminar ¶
Yau Mathematical Sciences Center, Tsinghua University
July 4, 2023