clustering – Plot data points according to the pairwise distance matrix


Consider eight data points. The following matrix (i.e., a symmetric matrix with the lower triangle elements) shows the pairwise distances between any two points.

  • 0
  • 11 0
  • 5 13 0
  • 12 2 14 0
  • 7 17 1 18 0
  • 13 4 15 5 20 0
  • 9 15 12 16 15 19 0
  • 11 20 12 21 17 22 30 0

Is it possible to plot all these eight data points in a two-dimensional space where the distance metric between every two points is the Euclidean distance and the above matrix can be satisfied? If yes, please draw all eight data points. If no, please state whether there exists a d-dimensional space where d > 2 such that the above matrix can be satisfied with the eight data points in this space. In this case, if there exists, please give the smallest value of d and give all eight data points in this d-dimensional space. Otherwise, please explain it.