TARDIS: Topological Algorithms for Robust DIscovery of Singularities#
The manifold hypothesis drives most of modern machine learning research, but what if you are not dealing with a manifold but a more complicated space? TARDIS uses a topology-driven approach to identify singularities in high-dimensional data sets at multiple scales, giving you a better overview of what is in your data.
How can TARDIS help you?#
Find out whether your data set contains singular regions, i.e. regions that are not adequately described by Euclidean space.
Discover whether dimensionality reduction algorithms are embedding your data correctly or resulting in distortion.
Assess the overall complexity of your data set in an unsupervised fashion.
Interested?#
Read more about TARDIS in our ICML paper and consider citing us:
@inproceedings{vonRohrscheidt23a,
title = {Topological Singularity Detection at Multiple Scales},
author = {von Rohrscheidt, Julius and Rieck, Bastian},
year = 2023,
booktitle = {Proceedings of the 40th International Conference on Machine Learning},
publisher = {PMLR},
series = {Proceedings of Machine Learning Research},
number = 202,
pages = {35175--35197},
editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan},
abstract = {The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct non-manifold structures, i.e. singularities, that can lead to erroneous findings. Detecting such singularities is therefore crucial as a precursor to interpolation and inference tasks. We address this issue by developing a topological framework that (i) quantifies the local intrinsic dimension, and (ii) yields a Euclidicity score for assessing the `manifoldness' of a point along multiple scales. Our approach identifies singularities of complex spaces, while also capturing singular structures and local geometric complexity in image data.}
}
Documentation#
Please find the API documentation and the module documentation below. As with a lot of academic code, TARDIS is a constant work in progress. Your contributions are more than welcome!