title: How do you manually compute for silhouette, cohesion and separation of Cluster
body: <p>Good day!</p>
  
  <p>I have been looking all over the Internet on how to compute for silhouette coefficient, cohesion and separation unfortunately, despite the resources, I just can't understand the formulas posted. I know that there are implementations of it in some tool, but I want to know how to manually compute them especially given a vector space model.</p>
  
  <h3>Assuming that I have the following clusters:</h3>
  
  <p>Cluster 1 ={{1,0},{1,1}} <br/>
  Cluster 2 ={{1,2},{2,3},{2,2},{1,2}}, <br/>
  Cluster 3 ={{3,1},{3,3},{2,1}}</p>
  
  <h3>The way I understood it according to [1] is that I have to get the average of the points per cluster:</h3>
  
  <p>C1 X = 1; Y = .5<br/>
  C2 X = 1.5; Y = 2.25<br/>
  C3 X = 2.67; Y = 1.67</p>
  
  <h3>Given the mean, I have to compute for my cohesion by Sum of Square Error (SSE):</h3>
  
  <p>Cohesion(C1) = (1-1)^2 + (1-1)^2 + (0-.5)^2 + (0-.5)^2 = <em>0.5</em> <br/>
  Cohesion(C2) = (1-1.5)^2 + (2-1.5)^2 + (2-1.5)^2 + (1-1.5)^2 + (2-2.5)^2 + (3-2.5)^2 + (2-2.5)^2 +(2-2.5)^2 = <em>2</em> <br/>
  Cohesion(C3) = (3-2.67)^2 + (3-2.67)^2 + (2-2.67)^2 + (1-1.67)^2 + (3-1.67)^2 + (1-1.67)^2 = <em>3.3334</em></p>
  
  <p>Cluster(C) = 0.5 + 2 + 3.3334 = <em>5.8334</em></p>
  
  <p><strong>My questions are: <br/></strong>
  1. Did I perform cohesion correctly? <br/>
  2. How do I compute for Separation? <br/>
  3. How do I compute for Silhouette Coefficient?</p>
  
  <p>Thank you.</p>
  
  <p><br/><strong>References:</strong><br/> [1] <a href="http://www.cs.kent.edu/~jin/DM08/ClusterValidation.pdf" rel="noreferrer">http://www.cs.kent.edu/~jin/DM08/ClusterValidation.pdf</a></p>