Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, November 09, 2017, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Patrick Schnider

Measures of depth for multiple points

Given a set P of n points in the plane, there are several concepts that measure how deep within the point set a query point p lies. One of the more famous of these concepts is the notion of Tukey depth: among all the halfplanes containing the query point p, consider one which contains the fewest points of P. The number of points of P that it contains is the Tukey depth of p. The famous centerpoint theorem assures the existence of some point, not necessarily from P, that has Tukey depth n/3. A point of high Tukey depth can be viewed as a median in higher dimensions, that is, as a representative of the whole point set. This talk is motivated by the following question: what if instead of one representative, we are instead interested in some small number of representatives? We consider several definitions of depth measures for multiple points instead of one and show the existence of deep points under these definitions. This is joint work with Alexander Pilz.

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