Fig. 4
From: Improved understanding of aqueous solubility modeling through topological data analysis
A visualisation of the Hausdorff distance. Let the red triangles be the subset X, and the orange circles be the subset Y. In b, the \(\epsilon\) illustrates the \(\sup _{y\in Y}\inf _{x\in X} d(x,y)\) part. It is the smallest number for which the disc of that radius around the orange circle farthest away from any of the triangles includes a triangle. To make the definition symmetric, this step is repeated for the triangles, and the maximum of the two radii is chosen