Cantelobre, Theophile;
Ciliberto, Carlo;
Guedj, Benjamin;
Rudi, Alessandro;
(2022)
Measuring dissimilarity with diffeomorphism invariance.
In: Chaudhuri, K and Jegelka, S and Song, L and Szepesvari, C and Niu, G and Sabato, S, (eds.)
Proceedings of the 39th International Conference on Machine Learning.
(pp. pp. 2572-2596).
PMLR 162
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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.
| Type: | Proceedings paper |
|---|---|
| Title: | Measuring dissimilarity with diffeomorphism invariance |
| Event: | 39th International Conference on Machine Learning (ICML) |
| Location: | Baltimore, MD |
| Dates: | 17 Jul 2022 - 23 Jul 2022 |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://proceedings.mlr.press/v162/cantelobre22a.h... |
| Language: | English |
| Additional information: | This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | Science & Technology, Technology, Computer Science, Artificial Intelligence, Computer Science |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10166870 |
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