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Manhattan distances, Kernels, and Metric Transforms.

Speaker: Tim Chu
Title: Manhattan distances, Kernels, and Metric Transforms.
Date: 25 Feb 2021 17:00-18:00 EST
Location: Zoom
Food: Self-prepared

Abstract: Take $n$ points in any dimension, compute the Manhattan distance between each pair of points, and take the $\pi/4$ power of each distance. The resulting distances will always be a Manhattan distance! Can you prove why?

In our work, we classify all functions $f$ that send Manhattan distances to Manhattan distances. We also classify all functions $f$ that send Manhattan distances to inner products, a fundamental question behind kernels in machine learning. The tools we use include the Hadamard transform, group representation theory, and more.

No background will be needed to enjoy this talk!