15.4 Exercises

EXERCISE 15.1   Apply the MDS method to the Swiss bank note data. What do you expect to see ?

EXERCISE 15.2   Using (15.6), show that (15.7) can be written in the form (15.2).

EXERCISE 15.3   Show that
  1. $b_{ii}=a_{\bullet \bullet}- 2a_{i \bullet};\
b_{ij}=a_{ij}-a_{i \bullet}-a_{\bullet j}+ a_{\bullet \bullet};
\ i \not= j $
  2. $\data{B}=\sum_{i=1}^p x_{i}x_{i}^{\top}$
  3. $\sum_{i=1}^n \lambda_{i}=\sum_{i=1}^n b_{ii}=\frac{1}
{2n \sum_{i,j=1}^n d_{ij}^{2}}$.

EXERCISE 15.4   Redo a careful analysis of the car marks data based on the following dissimilarity matrix:
  j 1 2 3 4
i   Nissan Wartburg BMW Audi
1 Nissan -      
2 Wartburg 2 -    
3 BMW 4 6 -  
4 Audi 3 5 1 -

EXERCISE 15.5   Apply the MDS method to the U.S. health data. Is the result in accordance with the geographic location of the U.S. states?

EXERCISE 15.6   Redo Exercise 15.5 with the U.S. crime data.

EXERCISE 15.7   Perform the MDS analysis on the Athletic Records data in Appendix B.18. Can you see which countries are ``close to each other''?