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Add Hausdorff Linkage #11

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kno10 opened this issue May 2, 2024 · 0 comments
Open

Add Hausdorff Linkage #11

kno10 opened this issue May 2, 2024 · 0 comments

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@kno10
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kno10 commented May 2, 2024

Hausdorff linkage is the twin of Minimax linkage, but much less widely known.

The name obviously comes from Hausdorff distance, a very classical measure for the distance of sets.

The objective is the "maximum minimum distance", i.e., choose the merge $A\cup B$ with the smallest
$$\max\left\{\max_{a\in A} \min_{b\in B} d(a,b), \max_{b\in B} \min_{a\in A} d(a,b)\right\}$$ and can be seen as finding the shortest edge such that every point from either set is connected to some point of the other set.

Basalto, Nicolas; Bellotti, Roberto; De Carlo, Francesco; Facchi, Paolo; Pantaleo, Ester; Pascazio, Saverio
Hausdorff clustering of financial time series
Physica A: Statistical Mechanics and Its Applications. 379 (2): 635–644.

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