title: Inter-Cluster and Intra-Cluster distances
body: <p>I have found the following formulas for Inter-Cluster and Intra-Cluster distances and I am not sure I understand how they work.</p>
  
  <p><img src="https://i.stack.imgur.com/mCPq6.png" alt="enter image description here"></p>
  
  <p>Inter-Cluster Distance</p>
  
  <p><img src="https://i.stack.imgur.com/nlV7Z.gif" alt="enter image description here"></p>
  
  <p>Shouldn't there be a square root in formulas above?</p>
  
  <p>Inter-Cluster and Intra-Cluster:</p>
  
  <p><img src="https://i.stack.imgur.com/BpRh2.gif" alt="enter image description here">
  <img src="https://i.stack.imgur.com/D9A6q.gif" alt="enter image description here"></p>
  
  <p>Why is there the j index starting from N+1? And not from 1 to N2?</p>
  
  <p>Which one is the correct one? Or are there any equivalencies? Or should I go for the distance between centroids for the inter cluster distance? Seems rather simple. What about the intra cluster distance?</p>
  
  <p>I find the wikipedia formulas <a href="http://en.wikipedia.org/wiki/Cluster_analysis#Internal_evaluation" rel="noreferrer">http://en.wikipedia.org/wiki/Cluster_analysis#Internal_evaluation</a> even harder to understand. </p>
  
  <p>I need to compute this distances in order to proper group colors in order to create a reduced color palette, so I'm thinking the more accurate these distances are, the more accurate the groupping (formula instead of distance between centroids distance for inter-cluster). The vectors are 3-dimensional(RGB components). </p>