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