fmcquillan99 edited a comment on issue #433: Kmeans: Add automatic optimal 
cluster estimation
URL: https://github.com/apache/madlib/pull/433#issuecomment-530576211
 
 
   From
   
https://scikit-learn.org/stable/auto_examples/cluster/plot_kmeans_silhouette_analysis.html
   the published results and the ones I get too are:
   ```
   Automatically created module for IPython interactive environment
   ('For n_clusters =', 2, 'The average silhouette_score is :', 
0.7049787496083262)
   ('For n_clusters =', 3, 'The average silhouette_score is :', 
0.5882004012129721)
   ('For n_clusters =', 4, 'The average silhouette_score is :', 
0.6505186632729437)
   ('For n_clusters =', 5, 'The average silhouette_score is :', 
0.5637646902619401)
   ('For n_clusters =', 6, 'The average silhouette_score is :', 
0.4504666294372765)
   ```
   
   When I run this example with the code in this PR, the cluster centers seem 
to be in exactly the same place for k=2,3,4 (diff centroids for k=5,6) but I 
get diff silh values: 
   ```
    k |    silhouette     
   ---+-------------------
    2 | 0.779349458639269
    3 | 0.686510525829679
    4 | 0.744861910083039
   ```
   
   diff chart:
   ```
   k    python/scikit-learn     madlib  delta   %diff
   2    0.7049787496    0.7793494586    0.07437070903   9.54%
   3    0.5882004012    0.6865105258    0.09831012462   14.32%
   4    0.6505186633    0.7448619101    0.09434324681   12.67%
   ```
   
   Both are using Euclidean distance.  Any idea what could account for the 
difference?

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