Evaluating Generative Adversarial Networks: A Topological Approach

Generative adversarial networks (GANs) are an approach to generative modelling using deep learning methods, such as convolution neural networks. Evaluating the performance of GANs has been a challenging task. In this paper, we will show how concepts from algebraic topology, and in particular persistent homology can be used for comparing the geometric and topological features of the latent manifold of real data with those of generated ones. We built a Vietoris-Rips complex to present persistence diagrams. As an evaluating metric between two diagrams of manifolds, we apply a framework which is a reformulation of the Wasserstein distance as an Optimal transport problem, called the WOT Distance. We compare the WOT Distance with the other topological structure metrics, Geometric score (GS) and Topological Distance (TD) on various data sets. Evaluation results demonstrate that our method achieves superior performance in GANs learning.