# Improving Relational Regularized Autoencoders with Spherical Sliced Fused Gromov Wasserstein

arXiv: https://arxiv.org/abs/2010.01787 · HTML: https://mlsanity.com/paper/2010.01787/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2020.

## Built on by (most cited first, 13 of 13)

- [Point-set Distances for Learning Representations of 3D Point Clouds](https://mlsanity.com/paper/2102.04014/) (2021)
- [Improving Mini-batch Optimal Transport via Partial Transportation](https://mlsanity.com/paper/2108.09645/) (2021)
- [Energy-Based Sliced Wasserstein Distance](https://mlsanity.com/paper/2304.13586/) (2023)
- [Spherical Sliced-Wasserstein](https://mlsanity.com/paper/2206.08780/) (2022)
- [Revisiting Sliced Wasserstein on Images: From Vectorization to Convolution](https://mlsanity.com/paper/2204.01188/) (2022)
- [Hierarchical Sliced Wasserstein Distance](https://mlsanity.com/paper/2209.13570/) (2022)
- [Amortized Projection Optimization for Sliced Wasserstein Generative Models](https://mlsanity.com/paper/2203.13417/) (2022)
- [On Transportation of Mini-batches: A Hierarchical Approach](https://mlsanity.com/paper/2102.05912/) (2021)
- [Nonparametric Generative Modeling with Conditional Sliced-Wasserstein Flows](https://mlsanity.com/paper/2305.02164/) (2023)
- [Markovian Sliced Wasserstein Distances: Beyond Independent Projections](https://mlsanity.com/paper/2301.03749/) (2023)
- [Gromov-Wasserstein Autoencoders](https://mlsanity.com/paper/2209.07007/) (2022)
- [Self-Attention Amortized Distributional Projection Optimization for Sliced Wasserstein Point-Cloud Reconstruction](https://mlsanity.com/paper/2301.04791/) (2023)
- [Fast Approximation of the Generalized Sliced-Wasserstein Distance](https://mlsanity.com/paper/2210.10268/) (2022)

## Abstract (arXiv)

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. Then, we introduce two variants of SSFG to improve its performance. The first variant, named mixture spherical sliced fused Gromov Wasserstein (MSSFG), replaces the vMF distribution by a mixture of von Mises-Fisher distributions to capture multiple important areas of directions that are far from each other. The second variant, named power spherical sliced fused Gromov Wasserstein (PSSFG), replaces the vMF distribution by a power spherical distribution to improve the sampling time in high dimension settings. We then apply the new discrepancies to the RAE framework to achieve its new variants. Finally, we conduct extensive experiments to show that the new proposed autoencoders have favorable performance in learning latent manifold structure, image generation, and reconstruction.