Hello! If you have come here, it means you might be interested in my extended abstract "Using topological autoencoders as a filtering function for global and local topology". I am looking for collaborators on this project to get this project into an actual paper, and if you are interested, do not hesitate to email me at [email protected]. It would be great to have a discussion!

Questions of interest:

• How do we best validate a Mapper graph?
• If we can validate the Mapper graph, can we prove which configuration of the Mapper is the best (choice of overlap, filtering function etc.)?

Best, Filip

This repository is for the experiments in the submission accepted to the workshop TDA and Beyond at NeurIps2020.

The experiments were run using Python 3.8.7.

Use your favorite virtual environment, and run

pip install -r requirements.txt

To run the experiments with default settings and simply reproduce the experiments, do:

python3 index.py

To output the results into a file, do:

python3 index.py --output_file FILEPATH

This will output your log output into a file which can then be used for analysis.

The experiments will take about an hour or so to with a computer with the following specifications.

• Macbook Pro
• MacOS Catalina 10.15.7 (19H2)
• 1,4 GHz Quad-Core Intel Core i5
• 16 GB 2133 MHz LPDDR3
• Intel Iris Plus Graphics 645 1536 MB

There are some possible arguments to use.

The seeds for these experiments are nested into the code, and the default seed is 125342.

The dataset used can be found in the folder experimentation/experiment_spheres, which is a dataset consisting of 11 different 100-dimensional hyper-spheres, 10 of them encompassed by another larger one. This dataset was created using functions available in the Topological Autoencoders repository.

To run these experiments on another dataset, your data should be divided as follows.

• train_dataset.csv : the training data points
• train_dataset_labels.csv : the manifold label groupings
• test_dataset.csv : the test data points
• test_dataset_labels.csv : the manifold label groupings of the test set
• latents.csv : latents of the test data points from inference of a topological autoencoder
• latents/tae_spheres.csv - tae test points but without the labels (latents.csv also contains the manifold labels).

Additionally, the latents/ folder which will be filled up with csv-files during the experiments. It contains tae_spheres.csv, which is the latents.csv without the labels.

The Topological Autoencoder model trained is available in models/topoAE_model.pth. The model was trained using python 3.8.5 and the versions:

• torch==1.4.0
• torchvision==0.5.0
• CUDA Version: 10.1

The code used to train the model is available in this Borgwardt lab repository.

If you'd like to cite this article, please cite it using this BibTex code:

@inproceedings{
cornell2020using,
title={Using topological autoencoders as a filtering function for global and local topology},
author={Filip Cornell},
booktitle={NeurIPS 2020 Workshop on Topological Data Analysis and Beyond},
year={2020},
url={https://openreview.net/forum?id=0V6WLosuIfJ}
}

This work was partially supported by Wallenberg Autonomous Systems Program (WASP).