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Regression Depth and Center Points

Nina Amenta·Marshall Bern·David Eppstein·Shang-Hua Teng
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Abstract

We show that, for any set of n points in d dimensions, there exists a hyperplane with regression depth at least ceiling(n/(d+1)). as had been conjectured by Rousseeuw and Hubert. Dually, for any arrangement of n hyperplanes in d dimensions there exists a point that cannot escape to infinity without crossing at least ceiling(n/(d+1)) hyperplanes. We also apply our approach to related questions on the existence of partitions of the data into subsets such that a common plane has nonzero regression depth in each subset, and to the computational complexity of regression depth problems.

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Nina Amenta, Marshall Bern, David Eppstein, Shang-Hua Teng. 1999-07-26. Regression Depth and Center Points. https://doi.org/10.1007/pl00009502

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