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The methods previously discussed

344 Feature selection and extraction

9.3.6 Summary

Algorithms for their implementation are readily available.


Multidimensional scaling

Multidimensional scaling 345

We begin our discussion with a description of one form of metric MDS, namely classical scaling.

If we impose the constraint that the centroid of the points xi; i D 1; : : : ; p, is at the origin, then (9.19) may be inverted to express the elements of the matrix T in terms of the dissimilarity matrix, giving

Ti j D �1 2[d2 i jd2 i:� d2 : jC d2 ::] (9.20)

where the columns of U are the eigenvectors of T and is a diagonal matrix of eigenvalues, ½1; : : : ; ½n. Therefore we take

X D U�


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the methods previously discussed
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