Existing approaches to data sketching are not guaranteed to yield structure-preserving data sketches. We introduce a novel randomized column sampling tool termed Spatial Random Sampling (SRS) in which data points are sampled based on their proximity to randomly sampled points on the unit sphere. The probability of sampling from a data cluster using SRS is proportional to its corresponding surface area on the unit sphere, independently of the size of the cluster population. SRS is shown to yield descriptive representations even if the data is highly unbalanced.