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I have to do a PCA in R for a project, but I have 300 data in 15 differents groups, and I want to find the reduced space which gives me the most variability between the groups and cluster my data in their own group ( so not between all the data) so I can do an analysis later while using these variables (I have 4000 very similar variables).

I know how to do the analysis when I want to cluster data that are not already in a group, but I don't know how to do it when I want to find out which variable can separate my groups the best.

The objective is that I use the reduced space that explain the most of the group variability to use them to do analysis, to observe if the data groups are really significantly different when I consider all the data, but I'm not sure if it's actually something possible to do with a ACP.

Thank you!

If it makes more sense, I want to see a result like that plot, but the cluster represent the groups I already have to see if they go upon each other, or if they are clearly different. I did a plot before that did not differenciate my data as their group and it was a mess, all mixed up

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  • $\begingroup$ Have a look at ICA. PCA looks at maximizing the variance while ICA search for the best split $\endgroup$
    – Mayeul sgc
    Commented Oct 18, 2022 at 1:25
  • $\begingroup$ I am not sure what method by itself does clustering and discriminant analysis together. Maybe a custom autoencoder? Anyway, here is a Python gist which performs linear discriminant analysis followed by k-means clustering. $\endgroup$
    – Galen
    Commented Oct 18, 2022 at 3:30
  • $\begingroup$ You might want to change the title because my understanding is that you do not need to cluster the data, rather you have clusters already given? $\endgroup$
    – Christian Hennig
    Commented Oct 18, 2022 at 10:33

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There are classical discriminant coordinates, closely related to Fisher's discriminant analysis, that project the data on a low (e.g., 2-d) hyperplane in such a way that ratio between the variation between class means and the variation within classes is maximum. This will give you an, in a well defined sense, optimal 2-d plot separating the clusters. There are also some versions of this taking robustness against outliers into account.

This is implemented in the R-functions plotcluster and discrcoord in my fpc package, see also references on the help pages.

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