Choosing the parameter of the Fermat distance: navigating geometry and noise
Abstract: The Fermat distance has been recently established as a valuable tool for machine learning tasks when a natural distance is not directly available to the practitioner or to improve the results given by Euclidean distances by exploding the geometrical and statistical properties of the dataset. This distance depends on a parameter $\alpha$ that significantly impacts the performance of subsequent tasks. Ideally, the value of $\alpha$ should be large enough to navigate the geometric intricacies inherent to the problem. At the same time, it should remain restrained enough to sidestep any deleterious ramifications stemming from noise during the distance estimation process.
We study both theoretically and through simulations how to select this parameter.
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Florent_Krzakala1
Submission Number: 1885
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