Multidimensional Scaling - Data Visualization - page 325

Figure . . Sammon mapping of the virus data: Hord - Hordeviruses, Tobr - Tobraviruses, Toba -
Tobaviruses, Furo - Furoviruses

inthespace.Aconfiguration issoughtsothat distances between pairsofpoints d rs

inthespacematch“aswellaspossible”theoriginal dissimilarities δ rs .Herematch-

ingmeans the rank orderof d rs matchestherank orderof δ rs asbestaspossible.

he matching of the distances d rs to the dissimilarities δ rs for a particular con-

figuration is measured by the STRESS (S), where

d rs

( d rs − )

r,s

S = ( . )

rs d rs

d rs

Here, ,also

known as isotonic regression. Details of this regression are not entered into here, but
an example can be seen in Fig. . , the Shepard plot. Further details can be found

is the primary monotone least-squares regression of d rs on δ rs