The methods previously discussed
344 Feature selection and extraction
9.3.6 Summary
Algorithms for their implementation are readily available.
| 9.4 |
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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 j� d2 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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