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enter image description hereI have used K-mean algorithm for clustering my data , and i have used Calinski-Harabasz as validity index measurement, the value of CH are :

 k=2 , CH= 13.41,  well separated cluster 
 k=4 , CH= 269.68   overlapped cluster 

The figure is k-mean algorithm with k=2 and CH= 13.41 and the second one is k-mean algorithm with k=4 , and CH = 269.68

i have added the 3rd figure in which the cluster are not separated well and the CH = 729 ??

enter image description here

the K=2 and the first figure is separated well cluster , while the second one is nonseparated well cluster

any suggestion please iam confused with CH behavior.

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  • $\begingroup$ There is a bouquet of questions to your case. 1) Were you doing K-means on the initial data or the two principal components you show? 2) Same Q about you doing CH calculation. 3) Your PC1 is so overwhelmingly bigger variance than PC2 that one wonders how you managed to get such clear oblong clusters by K-means. Did you standardize the data first? 4) If yes did you do same with computation of CH? Btw it is nice to give the data and to show the annotated code you used. $\endgroup$ – ttnphns Jan 4 '17 at 20:11
  • $\begingroup$ @ ttnphns : iam working on the PC's data , Why CH increasing when i increased the k number ? $\endgroup$ – Shwn Jan 4 '17 at 20:17
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    $\begingroup$ You didn't answer other points. In particular, (3). It is impossible to get 2 clusters like you showed with K-means because it produces approximately spherical clusters but your PCs are very different variance. So, did you standardize them before the clustering. If yes, why not show the standardized PCs? Did you compute CH on the standardized PCs either? (you should have to!) $\endgroup$ – ttnphns Jan 4 '17 at 20:23
  • $\begingroup$ @ttphns the data are normalized before the analyse $\endgroup$ – Shwn Jan 4 '17 at 20:33
  • $\begingroup$ OK then you ought to plot the pictures of the normalized data. Is CH computed on on those data problematic to you? If yes, may we ask you to post (or link to) the (normalized and clustered) dataset so that we could try to compute CH, to check? $\endgroup$ – ttnphns Jan 4 '17 at 20:37
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The problem are your plots.

Avoid plotting with distortion. If you plotted the data such that 1 unit on the x axis has the same size as 1 uniton the y axis, the result would likely be more comprehensible.

In your example, imagine the plot to be squeezed!

compared to

clearly, the bottom one does not separate the clusters well. The width of the clusters (about 40) is much larger than the separation between the cluster centers (about 2). In the top picture, thr width of the clusters is about 25,and the distance is over 10; so the top result is much better.

Don't let yourself be fooled by distorted plots!

I understand that the intuition here is different; but then you need to preprocess the data differently. As is, the distances clearly show the first result to be better.

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