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the methods previously discussed

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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