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I did a discriminant analysis for the validation of my cluster analysis. The cluster analysis is based on a PCA, so I used the components as the independant variables in the discriminant analysis. My question is: is there a restriction considering the number of the independant variables (components) compared to the number of my (cluster) groups?

Thanks a lot!

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  • $\begingroup$ How can DA validate the clusters? Please describe how you reason it in more details. $\endgroup$
    – ttnphns
    Commented Oct 30, 2013 at 17:32
  • $\begingroup$ Because it is frequently used in literature. $\endgroup$
    – cathy
    Commented Oct 31, 2013 at 3:57

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You can use the discriminant analysis to predict the cluster using your principal components as independent variables, so your model would be:

$Cluster=Component_1+Component_2,...,Component_n$

And no, you don't have a restriction on the number of components you can use in regards to the number of clusters you have. I would use them all. By means of cross validation I would measure how well this model (linear discriminant) predicts the cluster and if the accuracy is good you would know that the clusters are separable, crisp, which could be interpreted as cluster health. Note that you could use any classifier to do this. You could also directly use separability measures for this same purpose like Jeffries-Matusita or divergence.

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