# Revisiting Tree-Sliced Wasserstein Distance Through the Lens of the Fermat–Weber Problem

## Requirements
To install the required python packages, run
```
conda env create --file=environment.yaml
conda activate twd
cd power_spherical
```


Install `power_spherical` package:
```bash
cd power_spherical
pip install .
```

You may need to install additional requirements. Detail may be found in each experiment. 

## Included Experiments
* Gradient flow
* Denoising Diffusion
* Text Topic modeling 

## 2 experiments presented in the Appendix:
* Gradient Flow on images
* Point Cloud Gradient Flow