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Ward´s Linkage

Ward´s Linkage:

Ward´s linkage is a method for hierarchical cluster analysis . The idea has much in common with analysis of variance (ANOVA). The linkage function specifying the distance between two clusters is computed as the increase in the “error sum of squares” (ESS) after fusing two clusters into a single cluster. Ward´s Method seeks to choose the successive clustering steps so as to minimize the increase in ESS at each step.

The ESS of a set Math image of Math image values is the sum of squares of the deviations from the mean value or the mean vector ( centroid ). For a set Math image the ESS is described by the following expression:

Glossary Math


  • Math image is the absolute value of a scalar value or the norm (the “length”) of a vector.

Mathematically the linkage function – the distance between clusters Math image and Math image – is described by the following expression

Glossary Math


  • Math image is the combined cluster resulting from fusion clusters Math image and Math image ;
  • Math image is the error sum of squares describe above.

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