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Suppose I've data for 100 individuals for 5 variables, say Var1, Var2,...Var5. I run the cluster analysis using these 5 variables on these 100 rows & got 3 clusters. Now, I want to differentiate these 3 clusters based on 5 variables. That is, which among these 5 variables has been loaded more for which cluster, in order to get a meaningful interpretation of the clusters. Here I don't want to do PCA or other factor analysis.

I've heard that I can do that using discriminant analysis. Can anybody suggest me the method to do it?

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  • $\begingroup$ Check Wikipedia for a start. $\endgroup$ – user88 Jul 9 '11 at 9:46
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    $\begingroup$ You mean "discriminant analysis" aka "discriminant function analysis", don't you? However, this analysis won't tell you "which among these 5 variables has been loaded more for which cluster". Rather, it will tell you which among these 5 variables has been loaded more for which direction that pull apart clusters $\endgroup$ – ttnphns Jul 9 '11 at 9:53
  • $\begingroup$ @mbq: Thanks for your suggestion. @ttnphns: Yes I was taking about "discriminating function analysis" or "LDA". What actually I want to know is "how meaningfully I can interpret the clusters".In other words, how to label these clusters. I heard about LDA, so put that in the question. If there's any the method that answer my question I'll be grateful if somebody can suggest that to me. $\endgroup$ – Beta Jul 9 '11 at 10:03
  • $\begingroup$ So you want to describe your clusters, to interpret them. Discriminant analysis won't help you here as far as it decribes what differentiate clusters instead of what clusters are. You need simply to build and analyse profiles of the clusters - by your 5 variables and perhaps some background (not used in clustering) characteristics as well. $\endgroup$ – ttnphns Jul 9 '11 at 10:15
  • $\begingroup$ @ttnphns: Thank you! But I cann't able to analyze these cluster profiles. Is there any methodology to do it? Can you give me some reference(s)? $\endgroup$ – Beta Jul 9 '11 at 10:22
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A good idea might be to run some ANOVAS and MANOVAS on the cluster for whatever variables you're using. The variables that generated the cluster should generally yield significant differences, but if the 5 new vars you're incorporating were not the vars you used to generate the cluster solution, it's interesting to run them.

ANOVA, or a simple compare means test, maybe a t-test, will give you an F statistic, which is a relatively good indicator of how different each group [cluster in this case] is in terms of the relevant variables.

if your new 5 vars are categorical it might be as easy as a chi square test, but you might give multiple correspondence a try. multiple correspondence yields a biplot such that the distances between categories is an indicator of how much they tend to happen together, so if you have cluster 1 very near to 3 categories you conclude that those three categories are characteristic of cluster 1.

Or, you know, just describe the univariate statistics of each of your clusters.

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  • $\begingroup$ Thank you Tomas! This method is far more interesting from the ones I'm reading so far. $\endgroup$ – Beta Jan 2 '12 at 6:20

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