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According to the reference quoted below, when performing a classical MDS on a dataset, I have to compute a centered matrix $B$ based on the dissimilarity matrix and then to compute the eigen-decomposition $B = V \Lambda V^T$.

Then it is said (top page 320, step 4),

If the points were originally in a $p$-dimensional space, the first $p$ eigenvalues of $B$ are nonzero and the remaining $n-p$ are zero.

But what if $n<p$? Does it even have sense to try it?

And what does it mean to "discard the 0 eigenvalues from $\Lambda$"? Replace 0 by 0?

Reference :

amoeba
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Irminsul
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  • `But what about if n

    n points, it is possible. But is such a case, when you compute nXn distances the maximal intrinsic _dimensionality_ will be n, not p.

     – ttnphns Feb 09 '16 at 16:58
  • ...and when the space origin is the centroid of the points cloud, as it with the matrix B (the double-centration matrix), the maximal possible dimensionality is n-1. – ttnphns Feb 09 '16 at 17:07
  • Thank you ! And what about discarding eigenvalues ? Does it mean create a new matrix of size $n \times p$ ? – Irminsul Feb 10 '16 at 15:35
  • On this [thread](http://stats.stackexchange.com/q/14002/3277), pay attention to my as well as amoeba's answers. In particular, my answer links to a short a easy document with formulas describing Torgerson's MDS. – ttnphns Feb 10 '16 at 16:51

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