Measuring Dissimilarity with Diffeomorphism Invariance
Abstract
Measures of similarity (or dissimilarity) are a key ingredient to many machine learning algorithms. We introduce DID, a pairwise dissimilarity measure applicable to a wide range of data spaces, which leverages the data’s internal structure to be invariant to diffeomorphisms. We prove that DID enjoys properties which make it relevant for theoretical study and practical use. By representing each datum as a function, DID is defined as the solution to an optimization problem in a Reproducing Kernel Hilbert Space and can be expressed in closed-form. In practice, it can be efficiently approximated via Nystr{ö}m sampling. Empirical experiments support the merits of DID.
Cite
Text
Cantelobre et al. "Measuring Dissimilarity with Diffeomorphism Invariance." International Conference on Machine Learning, 2022.Markdown
[Cantelobre et al. "Measuring Dissimilarity with Diffeomorphism Invariance." International Conference on Machine Learning, 2022.](https://mlanthology.org/icml/2022/cantelobre2022icml-measuring/)BibTeX
@inproceedings{cantelobre2022icml-measuring,
title = {{Measuring Dissimilarity with Diffeomorphism Invariance}},
author = {Cantelobre, Théophile and Ciliberto, Carlo and Guedj, Benjamin and Rudi, Alessandro},
booktitle = {International Conference on Machine Learning},
year = {2022},
pages = {2572-2596},
volume = {162},
url = {https://mlanthology.org/icml/2022/cantelobre2022icml-measuring/}
}