  Automatic evaluation of the goodness of Generative Adversarial Networks
(GANs) has been a challenge for the field of machine learning. In this work, we
propose a distance complementary to existing measures: Topology Distance (TD),
the main idea behind which is to compare the geometric and topological features
of the latent manifold of real data with those of generated data. More
specifically, we build Vietoris-Rips complex on image features, and define TD
based on the differences in persistent-homology groups of the two manifolds. We
compare TD with the most commonly used and relevant measures in the field,
including Inception Score (IS), Frechet Inception Distance (FID), Kernel
Inception Distance (KID) and Geometry Score (GS), in a range of experiments on
various datasets. We demonstrate the unique advantage and superiority of our
proposed approach over the aforementioned metrics. A combination of our
empirical results and the theoretical argument we propose in favour of TD,
strongly supports the claim that TD is a powerful candidate metric that
researchers can employ when aiming to automatically evaluate the goodness of
GANs' learning.
