title: Kmeans elbow method not returning an elbow
body: <p>So following the example in documentation (<a href="http://www.scikit-yb.org/en/latest/api/cluster/elbow.html" rel="nofollow noreferrer">here</a>):</p>
  
  <blockquote>
    <p>The KElbowVisualizer implements the “elbow” method to help data scientists 
    select the optimal number of clusters by fitting the model with a range of 
     values for K. If the line chart resembles an arm, then the “elbow” (the 
    point of inflection on the curve) is a good indication that the underlying 
    model fits best at that point.</p>
  </blockquote>
  
  <p>What if there is no elbow in the chart? When I run the same code on my data set the output is:
  <a href="https://i.stack.imgur.com/4WQue.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/4WQue.png" alt="enter image description here"></a></p>
  
  <p>So the distortion score keeps increasing for every additional cluster.</p>
  
  <p>However, when I run another example of the elbow method, using the kmeans.intertia attribute:</p>
  
  <pre><code>sse = {}
  for k in range(1, 10):
      kmeans = KMeans(n_clusters=k, max_iter=1000).fit(testDF)
      testDF["clusters"] = kmeans.labels_
      #print(data["clusters"])
      sse[k] = kmeans.inertia_ # Inertia: Sum of distances of samples to their 
  closest cluster center
  plt.figure()
  plt.plot(list(sse.keys()), list(sse.values()))
  plt.xlabel("Number of cluster")
  plt.ylabel("SSE")
  plt.show()
  </code></pre>
  
  <p>The output is:</p>
  
  <p><a href="https://i.stack.imgur.com/mQYf4.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/mQYf4.png" alt="enter image description here"></a></p>
  
  <p>Which does have an elbow.</p>
  
  <p>What is the difference between these two methods? 
  Why is there no elbow on the first graph?</p>
  
  <p>According to documentation they both apply the same distance method, i.e. "Sum of squared distances of samples to their closest cluster center."</p>