CA Calculations Demonstrated with a Simple Example

To illustrate the typical steps of a hierarchical clustering procedure and to enable the reader to follow the calculations with a pocket calculator let us assume a very simple example with five objects (named K1 to KS) and two features (x and x2) each of equal dimension. 

The question is Which objects may be regarded as similar with respect to both features  

Because of the assumed equal dimensions the features will not be standardized. 

The distance matrix contains the EUCLIDean distances dik of all object pairs i and k. It is a symmetrical (5, 5)-matrix with dkl = dik, from which we write the upper triangle only  

The clustering algorithm starts by joining objects K1 and K3 because their distance is the least du = 1.41. 

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