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von Rohrscheidt, J.C. ; Rieck, B.

Topological Singularity Detection at Multiple Scales.

In: (Proceedings of Machine Learning Research). 2023. 35175-35197 (Proceedings of Machine Learning Research ; 202)
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.
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Publication type Article: Conference contribution
Corresponding Author
Conference Title Proceedings of Machine Learning Research
Quellenangaben Volume: 202, Issue: , Pages: 35175-35197 Article Number: , Supplement: ,
Non-patent literature Publications
Institute(s) Institute of AI for Health (AIH)