title: Finding the center of a cluster
body: <p>I have the following problem - made abstract to bring out the key issues.</p>
  
  <p>I have 10 points each which is some distance from the other. I want to </p>
  
  <ol>
  <li>be able to find the center of the cluster i.e. the point for which the pairwise distance to each other point is minimised, 
  <br> let p(j) ~ p(k) represent the pairwise distance beteen points j and k
  <br> p(i) is center-point of the cluster iff p(i) s.t. min[sum(p(j)~p(k))] for all 0 &lt; j,k &lt;= n where we have n points in the cluster  </li>
  <li>determine how to split the cluster in to two clusters once the number of data points in the cluster goes above some threshold t.</li>
  </ol>
  
  <p>This is not euclidean space. But the distances can be summarised as follows - p(i) is point i:</p>
  
  <pre><code>       p(1)    p(2)    p(3)    p(4)    p(5)    p(6)    p(7)    p(8)    p(9)    p(10)
  p(1)    0       2       1       3       2       3       3       2       3        4
  p(2)    2       0       1       3       2       3       3       2       3        4
  p(3)    1       1       0       2       0       1       2       1       2        3
  p(4)    3       3       2       0       1       2       3       2       3        4      
  p(5)    2       2       1       1       0       1       2       1       2        3   
  p(6)    3       3       2       2       1       0       3       2       3        4   
  p(7)    3       3       2       3       2       3       0       1       2        3  
  p(8)    2       2       1       2       1       2       1       0       1        2 
  p(9)    3       3       2       3       2       3       2       1       0        1
  p(10)   4       4       3       4       3       4       3       2       1        0 
  </code></pre>
  
  <p>How would I calculate which is the center point of this cluster?</p>