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

Abstract

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), Fr\'echet 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.

A Class of Topological Pseudodistances for Fast Comparison of Persistence Diagrams

“…6), we have birth times b = 0 by definition, and thus P D 0 is a 1-dimensional point cloud. In (Horak, Yu, and Salimi-Khorshidi 2021) a topology distance (TD) was proposed for comparing the 0dimensional part of PD's, and it improves upon earlier statistics such as Geometry Score (Khrulkov and Oseledets 2018) for GAN comparison. The main difference between W p and TD is that the latter is not invariant to relabelings of the points from the PD, whereas W p is.…”