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SUMMARY:Dimension reduction and distance learning: Classical methods and F
 ermat distance. - Matthieu Jonckheere (CNRS (Centre national de la recherc
 he scientifique))
DTSTART:20230523T123000Z
DTEND:20230523T133000Z
UID:TALK201568@talks.cam.ac.uk
DESCRIPTION:We first review some classical methods in machine learning to 
 deal with dimension reduction and distance learning.&nbsp\;\nWe then elabo
 rate on a new density-based estimator for weighted geodesic distances that
  takes into account the underlying density of the data\, and that is suita
 ble for nonuniform data lying on a manifold of lower dimension than the am
 bient space. The consistency of the estimator is proven using tools from f
 irst passage percolation. The macroscopic distance obtained depends on a u
 nique parameter and we discuss the choice of this parameter and the proper
 ties of the obtained distance for machine learning tasks.
LOCATION:Seminar Room 2\, Newton Institute
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