# Subsampling in Smoothed Range Spaces

@inproceedings{Phillips2015SubsamplingIS, title={Subsampling in Smoothed Range Spaces}, author={J. M. Phillips and Yan Zheng}, booktitle={ALT}, year={2015} }

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 approximations of these range spaces through $\varepsilon $-nets and $\varepsilon $-samples (aka $\varepsilon$-approximations). We characterize when size bounds for $\varepsilon $-samples on kernels can be extended…

## 2 Citations

Visualization of Big Spatial Data Using Coresets for Kernel Density Estimates

- Computer ScienceIEEE Transactions on Big Data
- 2021

A method for subsampling of spatial data suitable for creating kernel density estimates from very large data is described and it is demonstrated that it results in less error than random sampling.

Visualization of Big Spatial Data using Coresets for Kernel Density Estimates

- Computer Science2017 IEEE Visualization in Data Science (VDS)
- 2017

A method for subsampling of spatial data suitable for creating kernel density estimates from very large data is described and it is demonstrated that it results in less error than random sampling.

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