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Metric scaling uses a power transformation with a user-controlled exponent <math display="inline">p</math>: <math display="inline">d_{ij}^p</math> and <math display="inline">-d_{ij}^{2p}</math> for distance. In classical scaling <math display="inline">p=1.</math> Non-metric scaling is defined by the use of isotonic regression to nonparametrically estimate a transformation of the dissimilarities.
===Non-metric multidimensional scaling (
In contrast to metric MDS, non-metric MDS finds both a [[non-parametric]] [[monotonic]] relationship between the dissimilarities in the item-item matrix and the Euclidean distances between items, and the ___location of each item in the low-dimensional space. The relationship is typically found using [[isotonic regression]]: let <math display="inline">x</math> denote the vector of proximities, <math display="inline">f(x)</math> a monotonic transformation of <math display="inline">x</math>, and <math display="inline">d</math> the point distances; then coordinates have to be found, that minimize the so-called stress,
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