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.

提出了一种新的度量距离叫做拓扑距离，它可以比较真实数据和生成数据的几何和拓扑特征，同时也能够衡量生成对抗网络（GANs）的学习效果。在多种数据集上，与常用的测量方法进行了比较，证明了该方法是一种强有力的候选指标。

拓扑距离：一种基于拓扑的方法来评估生成对抗网络