Topology Distance: A Topology-Based Approach for Evaluating Generative Adversarial Networks

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