Quantifying similarity between high-dimensional single cell samples is challenging, and usually requires some simplifying hypothesis to be made. By transforming the high dimensional space into a high dimensional grid, the number of cells in each sub-space of the grid is characteristic of a given sample. Using a Hilbert curve each sample can be visualized as a simple density plot, and the distance between samples can be calculated from the distribution of cells using the Jensen-Shannon distance. Bins that correspond to significant differences between samples can identified using a simple bootstrap procedure.
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