Help to explanation of Hierarchical Clustering - Ward's method

[#1]

Hi all,

I try to understand the example of hierarchical clustering (picture below) with a distance matrix from JMP here: https://www.jmp.com/support/help/14/example-of-a-distance-matrix.shtml#316781

Applying Ward's formula (picture below) from here: https://www.jmp.com/support/help/14/distance-method-formulas.shtml#177809 

My question: How does JMP calculate the initial distance of 58,689863 between NY and Philadelphia by this formula? I have tried to apply the formula myself, but can't reach the same result. Any help is much appreciated. 

Cheers.

Best regards, Thomas

[#2]

In the example case you are giving it the distances, so JMP isn't really calculating the distances until clusters are created and it needs to calculate the distances between centroids.  So the expected distance should be 83 which is found in the flight data table.  This is the expected value, and it's exactly what you get when using any other method (Average, Centroid, Single, Complete).  Looking at all the distances the Ward method populates they are ~0.707 of what I'd expect them to be.  It appears JMP is applying some constant.  That said, it would be nice for someone on the JMP team to comment.

[#3]

Bonjour,

Je souhaiterais réaliser une CAH également et je me demande si vous aviez une réponse à cette question. Quelle constante applique JMP ?

Je vous remercie par avance.