I have a question about cluster analysis and I hope you can help me. I tested a sample of 30 patients with same scales (A, B, C, D, E, F) and I obtained two clusters, one with the results of two scales (A and B) and another with the results of other four different scales (C, D, E, F). I want to compare this two clusters that have a great similarity to find the overlapping of the clusters obtained in one and in the other one and validate the result. What kind of analysis should I do?
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1$\begingroup$ I don't understand. Did you (1) obtained two clusters of the 30 patients (some in one group, some in the other) using information from 6 variables (A–F) or (2) there are two cluster analyses, one using two variables (A,B) and the other based on patient values on four variables (C–F)? Do you want to compare (1) the two groups for their values on the 6 variables or (2) the results of different cluster analyses? $\endgroup$– FairMilesCommented Feb 13, 2013 at 19:02
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$\begingroup$ I explain better. I had tested 30 patients with three scales, the last one is made of four variables. Than I did a cluster analysis of the 30 patients with the first two scales (A e B, two variables) and I obtain the first dendrogram. After this I did a cluster analysis of the 30 patients with the third scale that contain four variables (C,D,E,F) using the same method and distance of the first analysis and I obtain the second dendrogram. $\endgroup$– M_NCommented Feb 13, 2013 at 19:13
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$\begingroup$ Now I want to calculate the overlapping of this two dendrogram, that have many cluster in common, for example, the first cluster of the first dendrogram contain the patients 1,2,3 and the second cluster of the second dendrogram contain the patient 1,2,3,4. I would like to calculate this overlapping and show that this is not casual. $\endgroup$– M_NCommented Feb 13, 2013 at 19:14
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$\begingroup$ Maybe something like a cross-clasification? Do the clusters have some attached meaning/interpretation (high, low, ill, normal)? If you want to compare the scales themselves, have you thought in comparing them directly (without forming groups first) like in a canonical correlation or a correlation among PCA first axes? $\endgroup$– FairMilesCommented Feb 13, 2013 at 19:35
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$\begingroup$ Look for the "multiclus" workshops, and browse through these publications. They may point you to relevant methods. $\endgroup$– Has QUIT--Anony-MousseCommented Feb 13, 2013 at 19:41
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1 Answer
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From your question alone, the partition you consider seems to be flat. But from your additional comments, I understand you are dealing with hierarchical clusters. So I am considering the latter here. For the former, many measures already exist to compare partitions such as the (Adjusted) Rand index, or the Normalized Mutual Information. See Comparing Clusterings - An Overview.
For the comparison of hierarchical clusters, there seems to be quite a literature, too. As proposed in this Stack Overflow post, one naïve method can be to process a 'flat' measure such as those cited above (ARI, NMI...), for each level of both dendrograms, and then combine them (e.g. average) to obtain an overall score.
Otherwise, you'll find more advanced methods online, such as A Method for Comparing Two Hierarchical Clusterings or Multilevel comparison of dendrograms: a new method with an application for genetic classifications.
answered Jun 4, 2013 at 16:53