# Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis

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### Cites methods from "Multidimensional scaling by optimiz..."

...These methods also bear close relationships to more classic approaches to spectral clustering [23], multi-dimensional scaling [19], as well as the PageRank algorithm [25]....

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### Cites background or methods from "Multidimensional scaling by optimiz..."

...If we adopt the primary approach to ties described in [ 7 ], that is, if the only constraints on the d, are those in Section 1, then this preprocessing simply consists of arranging the dissimilarities within each tie-block in such a way that the distances d, within that block form an increasing sequence....

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...In a companion paper [ 7 ] we describe the rationale for our approach to scaling, which is related to that of Shepard [9]....

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...In [ 7 ] we suppose that there are n objects 1, ... , n, and Chat we have experimental values 8~; of dissimilarity between them....

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##### References

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### "Multidimensional scaling by optimiz..." refers background or methods in this paper

...= stress of the fixed configuration xl , ---, x. = min numbe ra ~i i ~ -- ~ satisfying (Mon) We point out that this minimization is accomplished not by varying a trim set of values for the d~;, but rather by a rapid, efficient algorithm which is described in detail in the companion paper [12]....

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...Finally, at the practical level, we give in a companion paper [12] all the important details necessary to perform this iterative technique successfully....

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### "Multidimensional scaling by optimiz..." refers methods in this paper

...[For proof of this fact, see for example Kolmogorov and Fomin ([ 11 ], pp. 19-22) or Hardy, Littlewood, and Polya ([8], pp. 30-33).] If r = 2, then d~ is ordinary Euclidean distance....

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1,551 citations