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

where

is the absolute value of a scalar value or the norm (the "length") of a vector.

Mathematically the linkage function - the distance between clusters and - is described by the following expression

where

is the combined cluster resulting from fusion clusters and ;

This course will teach you how to use various cluster analysis methods to identify possible clusters in multivariate data. Methods discussed include hierarchical clustering, k-means clustering, two-step clustering, and normal mixture models for continuous variables.