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===Classical multidimensional scaling===
It is also known as '''Principal Coordinates Analysis''' (PCoA), Torgerson Scaling or Torgerson–Gower scaling. It takes an input matrix giving dissimilarities between pairs of items and outputs a coordinate matrix whose configuration minimizes a [[loss function]] called ''strain.'',<ref name="borg"/>
<math display=block>\text{Strain}_D(x_1,x_2,...,x_N)=\Biggl(\frac{ \sum_{i,j} \bigl( b_{ij} - x_i^T x_j \bigr)^2}{\sum_{i,j}b_{ij}^2} \Biggr)^{1/2},</math>
where <math>x_{i}</math> denote vectors in ''N''-dimensional space, <math>x_i^T x_j </math> denotes the scalar product between <math>x_{i}</math> and <math>x_{j}</math>, and <math>b_{ij}</math> are the elements of the matrix <math>B</math> defined on step 2 of the following algorithm, which are computed from the distances.
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