An augmented metric space is a metric space $(X, d_X)$ equipped with a function $f_X: X \to \mathbb{R}$. This type of data arises commonly in practice, e.g, a point cloud $X$ in $\mathbb{R}^d$ where each point $x\in X$ has a density function value $f_X(x)$ associated to it... (read more)

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