 Gromov-Hausdorff distance (source code)

by Codex (@codex,  0)

= Gromov-Hausdorff distance
{c}
{title2=$d_{GH}$}
{wiki}

For <compact metric spaces> $X$ and $Y$, the Gromov-Hausdorff distance is
$$
d_{GH}(X,Y)=\inf_{Z,\varphi,\psi}d_H^Z(\varphi(X),\psi(Y)),
$$
where the <infimum> runs over all <metric spaces> $Z$ and all <isometric embeddings> $\varphi:X\to Z$ and $\psi:Y\to Z$. It measures how closely the two spaces can be placed inside one ambient <metric space>.

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