# Spatial Random Sampling: A Structure-Preserving Data Sketching Tool

## TL;DR

This paper introduces Spatial Random Sampling (SRS), a novel data sketching method that preserves data structure by sampling based on proximity to random points on the unit sphere, ensuring balanced and descriptive data representations.

## Contribution

The paper proposes SRS, a new randomized sampling technique that maintains data structure and balances cluster representation regardless of cluster size or linear dependence.

## Key findings

- SRS provides balanced data sketches proportional to cluster surface areas.
- SRS outperforms traditional sampling in preserving data structure.
- SRS is effective for large-scale data analysis.

## Abstract

Random column sampling is not guaranteed to yield data sketches that preserve the underlying structures of the data and may not sample sufficiently from less-populated data clusters. Also, adaptive sampling can often provide accurate low rank approximations, yet may fall short of producing descriptive data sketches, especially when the cluster centers are linearly dependent. Motivated by that, this paper introduces a novel randomized column sampling tool dubbed Spatial Random Sampling (SRS), in which data points are sampled based on their proximity to randomly sampled points on the unit sphere. The most compelling feature of SRS is that the corresponding probability of sampling from a given data cluster is proportional to the surface area the cluster occupies on the unit sphere, independently from the size of the cluster population. Although it is fully randomized, SRS is shown to provide descriptive and balanced data representations. The proposed idea addresses a pressing need in data science and holds potential to inspire many novel approaches for analysis of big data.