Hausdorff GAN: Improving GAN Generation Quality With Hausdorff Metric

Data usually resides on a manifold, and the minimal dimension of such a manifold is called its
intrinsic dimension
. This fundamental data property is not considered in the generative adversarial network (GAN) model along with its its variants; such that original data and generated data often hold different
intrinsic dimensions
. The different
intrinsic dimensions
of both generated and original data may cause generated data distribution to not match original data distribution completely, and it certainly will hurt the quality of generated data. In this study, we first show that GAN is often unable to generate simulation data, holding the same
intrinsic dimension
as the original data with both theoretical analysis and experimental illustration. Next, we propose a new model, called
Hausdorff
GAN, which removes the issue of different
intrinsic dimensions
and introduces the
Hausdorff
metric into GAN training to generate higher quality data. This provides new insights into the success of
Hausdorff
GAN. Specifically, we utilize a mapping function to map both original and generated data into the same manifold. We then calculate the
Hausdorff
distance to measure the difference between the mapped original data and the mapped generated data, toward pushing generated data to the side of original data. Finally, we conduct extensive experiments (using MNIST, CIFAR10, and CelebA datasets) to demonstrate the significant performance improvement of the
Hausdorff
GAN in achieving the largest
Inception Score
and the smallest Frechet inception distance (FID) score as well as producing diverse generated data at different resolutions.