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Here is the basic SKLearn tutorial on K-means.

They run PCA and then do K-means on reduced data. Can it radically affect the result? Will we get totally different clusters if we apply PCA on already clustered data?

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    $\begingroup$ The topic "k means after PCA" is like "is there life after love" - asked and answered numerous times on this site. Please try to search and read, before asking. $\endgroup$
    – ttnphns
    Commented Nov 21, 2017 at 9:34
  • $\begingroup$ See this answer which in summary says: PCA mitigates the effect of outliers and hence in the presence of outliers, the results could be radically different. stats.stackexchange.com/a/12856/73547 $\endgroup$
    – discipulus
    Commented Feb 2, 2019 at 4:51

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Yes, it can radically affect the result.

You can get completely orthogonal clusters if the variances of the components are different by a large factor.

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