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

TL;DR

This paper introduces the use of Signature Transform and log-signature to evaluate GAN-generated image distributions, offering faster, CPU-based measures of convergence and novel visualization techniques.

Contribution

It pioneers RMSE and MAE Signature metrics, introduces analytical statistical measures for GAN goodness of fit, and proposes a PCA adaptive t-SNE for improved data visualization.

Findings

Signature-based metrics are computationally efficient and effective.

New analytical measures provide reliable assessment of GAN convergence.

Proposed visualization method enhances understanding of data distributions.

Abstract

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.