# Calinski-Harabasz cluster evaluation

I 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 ??

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.

• 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. – ttnphns Jan 4 '17 at 20:11
• @ ttnphns : iam working on the PC's data , Why CH increasing when i increased the k number ? – Shwn Jan 4 '17 at 20:17
• 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!) – ttnphns Jan 4 '17 at 20:23
• @ttphns the data are normalized before the analyse – Shwn Jan 4 '17 at 20:33
• 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? – ttnphns Jan 4 '17 at 20:37