More precisely, if I conduct a cmdscale (classical multidimensional scaling) on an Euclidean distance matrix by considering $n$ observations of $p$ variables i.e. $D_{ij}=\sqrt{ \sum_p (x_{ip} - x_{jp})^2}$ with $i$ and $j \in n$:

  1. Must the distributions of $x_p$ be normal (like in a PCA) ?
  2. And actually, if $p=1$, does it then mean something to conduct the PCoA and then do a clustering analysis?
  • $\begingroup$ Re 1: As far as I know, PCA does not require normality. $\endgroup$ – Richard Hardy May 4 '19 at 16:16
  • $\begingroup$ What is a "cmdscale"? $\endgroup$ – whuber May 4 '19 at 16:17
  • $\begingroup$ @RichardHardy Ok thx. So it means that I just have to find the appropriate transformation so that outliers do not outweight the PCoA, right ? $\endgroup$ – Romain May 4 '19 at 16:21
  • $\begingroup$ @RichardHardy Wait, sorry I just realized. I think a PCA supposes normality when working out the covariances, but for the PCoA I don't know... $\endgroup$ – Romain May 4 '19 at 16:23
  • 1
    $\begingroup$ I think PCA is a purely algebraic procedure with no assumptions, bar those that make PCA algebraically feasible. Assumptions like normality are needed for proving properties of statistical procedures, not algebraic ones. $\endgroup$ – Richard Hardy May 4 '19 at 17:15

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