title: Why is the line of wss-plot (for optimizing the cluster analysis) looks so fluctuated?
body: <p>I have a cluster plot by R while I want to optimize the "elbow criterion" of clustering with a wss plot, so I drew a wss plot for my cluster, but is looks really strange and I do not know how many elbows should I cluster, anyone could help me?</p>
  
  <p>Here is my data:<br></p>
  
  <pre><code>Friendly&lt;-c(0.533,0.854,0.9585,0.925,0.9125,0.9815,0.9645,0.981,0.9935,0.9585,0.996,0.956,0.9415)
  Polite&lt;-c(0,0.45,0.977,0.9915,0.929,0.981,0.9895,0.9875,1,0.96,0.996,0.873,0.9125)
  Praising&lt;-c(0,0,0.437,0.9585,0.9415,0.9605,0.998,0.998,0.8915,1,1,1,0.977)
  Joking&lt;-c(0,0,0,0.617,0.942,0.9665,0.9935,0.992,0.935,0.987,0.975,0.9915,0.9665)
  Sincere&lt;-c(0,0,0,0,0.617,0.8335,0.985,0.9895,0.977,0.9205,1,0.9585,0.8895)
  Serious&lt;-c(0,0,0,0,1,0.642,0.975,0.9605,0.9645,0.9895,0.8125,0.9605,0.925)
  Hostile&lt;-c(0,0,0,0,0,0,0.629,0.656,0.948,0.9705,0.9645,0.998,0.9685)
  Rude&lt;-c(0,0,0,0,0,0,0,0.687,0.979,0.954,0.954,0.996,0.956)
  Irony&lt;-c(0,0,0,0,0,0,0,0,0.354,0.9815,0.996,1,0.971)
  Insincere&lt;-c(0,0,0,0,0,0,0,0,1,0.396,0.996,0.9915,0.9415)
  Commanding&lt;-c(0,0,0,0,0,0,0,0,0,1,0.462,0.9605,0.9165)
  Suggesting&lt;-c(0,0,0,0,0,0,0,0,0,0,0,0.867,0.775)
  Neutral&lt;-c(0,0,0,0,0,0,0,0,0,0,0,0,0.283)
  
  data &lt;- data.frame(Friendly,Polite,Praising,Joking,Sincere,Serious,Hostile,Rude,Blaming,Insincere,Commanding,Suggesting,Neutral)
  </code></pre>
  
  <p>And here is my code of clustering: the method is given by Gavin in the last line of :<a href="https://stackoverflow.com/questions/25959385/how-to-draw-the-plot-of-within-cluster-sum-of-squares-for-a-cluster">How to draw the plot of within-cluster sum-of-squares for a cluster?</a></p>
  
  <pre><code>##cluster analysis
  dist&lt;-as.dist(data)
  hc&lt;-hclust(dist, method="average")
  plot(hc, main="", sub='Method="Average"', ann=T, axes=T, hang=0.2)
  ##draw a wss plot
  res &lt;- sapply(seq.int(1, 13), wrap, h = hc, x = data) 
  plot(seq_along(res), res, type="b", pch=19)
  </code></pre>
  
  <p>But it looks like this, anyone can explain why this happened and how to decide the "elbow criterion"?
  <img src="https://i.stack.imgur.com/TekDx.png" alt="enter image description here"></p>