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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.
The text was updated successfully, but these errors were encountered:
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.
The text was updated successfully, but these errors were encountered: