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In this paper, we bring forward the use of the recently developed SignatureTransform as a way to measure the similarity between image distributions andprovide detailed acquaintance and extensive evaluations. We are the first topioneer RMSE and MAE Signature, along with log-signature as an alternative tomeasure GAN convergence, a problem that has been extensively studied. We arealso forerunners to introduce analytical measures based on statistics to studythe goodness of fit of the GAN sample distribution that are both efficient andeffective. Current GAN measures involve lots of computation normally done atthe GPU and are very time consuming. In contrast, we diminish the computationtime to the order of seconds and computation is done at the CPU achieving thesame level of goodness. Lastly, a PCA adaptive t-SNE approach, which is novelin this context, is also proposed for data visualization.

Signature and Log-signature for the Study of Empirical Distributions Generated with GANs