A common approach to clustering is called multidimensional scaling (MDS). To apply MDS, we rank each pair of objects we want to cluster from least similar (higher number) to most similar (lower number). For example, in the file P08_42.xlsx, we compared the similarity of 10 banks and found banks 5 and 10 to be most similar and banks 9 and 10 to be least similar. We now assign a location in the x-y plane to each bank. The goal is to ensure that when we rank the distances between pair of banks, the ordering of these distances matches (as closely as possible) the similarity rankings of the banks.

a. Constrain each bank to have an x and y coordinate between -1 and +1 and determine the “location” of each bank.

b. How does this method lead to a natural clustering of banks?

c. How could you determine whether you need more than two dimensions to adequately locate the banks?