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I just attempted implementations of Ward linkage and UPGMA linkage, as well as Pearson and Euclid similarity coefficients. To my surprise, both similarity coefficients gave the same clustering with the Ward linkage. Should this be the case? Is this an indication that I made a mistake in my implementation?

I can tell you that, although the clustering was the same, the depth of the clusters were different. I can also tell that the similarity coefficients gave different clustering with the UPGMA linkage.

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  • $\begingroup$ Try to search for "Ward clustering" on this site. The only geometrically correct input for Ward is squared euclidean distances. What is Euclid similarity can you show the formula? $\endgroup$
    – ttnphns
    Jun 15, 2013 at 7:48
  • $\begingroup$ Thanks a lot! I tried squared Euclidian distance and it solved another problem I was having. Namely, so-called 'reversals' or non-monotonicity. I am feeling somewhat reassured that my Ward implementation is correct. Would it be correct to say that, in the case of Ward linkage, unlike UPGMA, the similarity coefficient does not affect which two clusters get combined, but it does affect what new similarity coefficient value gets assigned to the new combined cluster? $\endgroup$
    – Jared Olerend
    Jun 17, 2013 at 22:29
  • $\begingroup$ Ward combines such two clusters i and j that the SS (of deviations from centroid) in the combined cluster ij is minimally greater than SSi+SSj. SS in a cluster is equal to the sum of squared euclidean distances b/w the objects of the cluster devided by the number of the objects. $\endgroup$
    – ttnphns
    Jun 18, 2013 at 7:16

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The choice of distance function depends on your data.

There is no general rule based on the linkage you want.

Probably your test data was too simple in structure to expose the two linkage methods.

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  • $\begingroup$ Thanks, my test data has 192 entries and 26 characteristics. Also, the difference I am trying to expose is between two distance functions using a single linkage method. If I give my user the choice between two distance functions and they give the "same" result, this may be alarming to my user and it may be an indication that I should limit the choices in the case of Ward linkage. On the other hand, this could be an indication that I made a mistake in my implementation. By the way, when I say "same", I mean the clustering is the same, but the depth of the clusters is different. $\endgroup$
    – Jared Olerend
    Jun 12, 2013 at 18:10
  • $\begingroup$ Well, try other clustering software and see if it returns the same result to validate your implementation. And try other data sets, if this holds for any data set... $\endgroup$
    – Has QUIT--Anony-Mousse
    Jun 12, 2013 at 21:02

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