Subsampling in Smoothed Range Spaces

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Subsampling in Smoothed Range Spaces
We consider smoothed versions of geometric range spaces, so an element of the ground set (e.g. a point) can be contained in a range with a non-binary value in [0, 1]. Similar notions have been considered for kernels; we extend them to more general types of ranges. We then consider approximation of these range spaces through εnets and ε-samples (aka ε-approximations). We characterize when size bounds for ε-samples on kernels can be extended to these more general smoothed range spaces. We also describe new generalizations for ε-nets to these range spaces and show when results from binary range spaces can carry over to the smoothed ones.
Jeff M. Phillips, Yan Zheng
Added 15 Apr 2016
Updated 15 Apr 2016
Type Journal
Year 2015
Where ALT
Authors Jeff M. Phillips, Yan Zheng
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