Preface to First Edition - lib

SUMMARY 311ExercisesEx. 17.1 The data in Table 17.3 shows road distances between 21 Europeancities. Apply classical scaling to the matrix and compare the plotted twodimensionalsolution with a map of Europe.Ex. 17.2 In Table 17.4 (from Kaufman and Rousseeuw, 1990), the dissimilaritymatrix of 18 species of garden flowers is shown. Use some form ofmultidimensional scaling to investigate which species share common properties.Ex. 17.3 Consider 51 objects O 1 , ...,O 51 assumed to be arranged along astraight line with the jth object being located at a point with coordinatej. Define the similarity s ij between object i and object j as⎧9 if i = j8 if 1 ≤ |i − j| ≤ 3⎪⎨7 if 4 ≤ |i − j| ≤ 6s ij =· · ·1 if 22 ≤ |i − j| ≤ 24⎪⎩0 if |i − j| ≥ 25Convert these similarities into dissimilarities (δ ij ) by usingδ ij = √ s ii + s jj − 2s ijand then apply classical multidimensional scaling to the resulting dissimilaritiymatrix. Explain the shape of the derived two-dimensional solution.© 2010 by Taylor and Francis Group, LLC