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Dimension reduction and distance learning: Classical methods and Fermat distance.

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DDE - The mathematical and statistical foundation of future data-driven engineering

We first review some classical methods in machine learning to deal with dimension reduction and distance learning.  We then elaborate on a new density-based estimator for weighted geodesic distances that takes into account the underlying density of the data, and that is suitable for nonuniform data lying on a manifold of lower dimension than the ambient space. The consistency of the estimator is proven using tools from first passage percolation. The macroscopic distance obtained depends on a unique parameter and we discuss the choice of this parameter and the properties of the obtained distance for machine learning tasks.

This talk is part of the Isaac Newton Institute Seminar Series series.

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