This is a dendrogram resulting from a hierarchical clustering using SPSS.
enter image description here

I thought the clustering is done in the following way. I would like to know if the way I am interpreting is correct.

First a and c are clustered to form say c1 cluster.
Then c1 is clustered with b to form c2 cluster. Then c2 with d to form c3 cluster. Then c3 would cluster with e to create one final cluster?

Is it like this or does a,b,c all form c1 cluster and then c1 clusters with d to form c2 cluster and finally c2 clusters with e?

So does it always come up with a final single cluster ?
Can't we have say a,b,c form one cluster and d,e another cluster. Like that can't we have two clusters?
Objects in one cluster has similar properties or behavior right? They are clustered based on some common characteristics.

  • $\begingroup$ So does it always come up with a final single cluster? Yes. Hierarchical clustering merges clusters until the end. It is you who decides where to "cut" the tree to leave "good" clusters. In your example, the first two steps combined a, b and c (the three are probably identical objects). Then adds d. On the last step, e joins. I would say you have two "good" clusters: (a+b+c+d) and e. $\endgroup$ – ttnphns Sep 21 '15 at 6:15
  • $\begingroup$ @ttnphns Is there a way to measure how strong a particular cluster is? Like for example 80% sure that the variables a,b,c,d,e form a cluster $\endgroup$ – clarkson Sep 21 '15 at 8:33
  • $\begingroup$ Yes, the "validity" of a clustering solution can be measured in a variety of ways. 1) Numerous so called internal clustering criterions; 2) External clustering criterions; 3) Interpretability; 4) Visual inspection. Please start with Wikipedia article on clustering and then proceed to special literature. Many things can be learned also by reading other CV questions tagged clustering. $\endgroup$ – ttnphns Sep 21 '15 at 8:40

In the dendrogram, a strong cluster can be seen as one that is stable for a long time before new members are added, as we move along the x-axis. So when there is a large range of inter-cluster distances where no new clusters are formed by merging, we can 'cut' the tree there and stop the clustering. As @ttnphns commented, (a+b+c+d) and (e) are to strong clusters for this reason, with the inter-cluster distance ranging from c.2.5 to 25 units.

You also ask if "objects in one cluster have similar properties or behavior". This is usually true, and is the usual reason for attempting cluster analysis. However, single-linkage hierarchical clustering can be mislead by some data sets, forming long chains of points that don't really have much in common. So some post hoc inspection is usually required to identify what, if any, features they have in common.


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