Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, April 25, 2023, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Simon Weber

Reducing Nearest Neighbor Training Sets Optimally and Exactly

In nearest-neighbor classification, a training set P of points in R^d with given classification is used to classify every point in R^d: Every point gets the same classification as its nearest neighbor in P. Recently, Eppstein [SOSA'22] developed an algorithm to detect the relevant training points, those points p∈P, such that P and P∖{p} induce different classifications. We investigate the problem of finding the minimum cardinality reduced training set P′⊆P such that P and P′ induce the same classification. We show that the set of relevant points is such a minimum cardinality reduced training set if P is in general position. Furthermore, we show that finding a minimum cardinality reduced training set for possibly degenerate P is in P for d=1, and NP-complete for d≥2. This is work based on the semester thesis of Josiah Rohrer.

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