title: K-means clustering using Inversion Distance
body: <p>First thing, I'm trying to figure out how to apply this algorithm to solve a homework project. So, I'm not looking for the homework solution, just help completing my algorithm which solves the problem.</p>
  
  <p>I am trying to use K-means clustering to cluster a large set (2^6) of arrays. These arrays are unique permutations of the sequence [0,1,2...31]. However, instead of using euclidean distance, I need to use inversion distance.</p>
  
  <p>My first step in k-means is to choose k=10 random points from the data set. I then calculate the inversion distance of each value in the data set to each of the random k-points. This gives the initial clustering.</p>
  
  <p>Now, I cannot figure out how to convert the next step from euclidean distance to inversion distance. How can I find the center of each of these clusters (in terms of inversion distance) so I can repeat the clustering step?</p>
  
  <p><br><br>
  As a companion question, is euclidean distance a good approximation for (or equivalent) inversion distance? I do not believe it is, but I am not sure how to go about proving it.</p>
  
  <p>Thanks to all in advance.</p>