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In this work, we explore the potential of applying a  type of survival of empty space function to a high dimensional dataset after running it through UMAP. In doing so, we get relevant information on the inner geometric structure of the different clusters obtained from the original data set. Our function is built from the geometry of the data set alone. It looks at different resolutions, the alpha shape that will eventually cover the set. Finally, it will compare its area to that of the smallest window containing the data. The window can be the bounding box or the convex-hull of the data. We apply this to a dataset of human activities. The results show that  different activities have different internal geometric structures, in particular the walking activities.

Survival of Empty Space Function, UMAP, Alpha Shape, CSR Process