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.


Read more about TARDIS in our ICML paper and consider citing us:

  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.}


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!

Indices and tables#