Improving Relational Regularized Autoencoders with Spherical Sliced Fused Gromov Wasserstein

Understand

Relational regularized autoencoder (RAE) is a framework to learn the distribution of data by minimizing a reconstruction loss together with a relational regularization on the latent space.

• A recent attempt to reduce the inner discrepancy between the prior and aggregated posterior distributions is to incorporate sliced fused Gromov-Wasserstein (SFG) between these distributions.
• That approach has a weakness since it treats every slicing direction similarly, meanwhile several directions are not useful for the discriminative task.
• To improve the discrepancy and consequently the relational regularization, we propose a new relational discrepancy, named spherical sliced fused Gromov Wasserstein (SSFG), that can find an important area of projections characterized by a von Mises-Fisher distribution.