replicability and stability of clustering by K means using HP nodes sas Miner

[HLuffy]

I create a n clusters using SAS miner HP cluster nodes( K means ). but every time I try to replicate the same clusters it give a different clusters. even using EG with different initializations give me different clusters.  my questions are :

1- Is  there a way to fix this clusters and make it my work replicable?  

2- If I can't fixe my clusters is there a way to test the stability of my clusters using for example an overlap rate and said after 75 % we can said that the clusters are stable? 

3- I couldn't find any straight forward answer for the stability of the clusters and how it's important. can we speak about the stability of clustering in this situation? is it very important to test the stability before use the clusters? which measures can do that ? is there any nodes in sas miner can do that?

I'm a little bit lost with this question of the stability. thank you for your understanding !!

[Reeza]

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K-Means clustering doesn't have a single unique solution, more so, there's a set of possible solutions and it's about picking one that makes the most sense for your use case. Especially if you change the initialization parameters then the clusters will be different. 

If your clusters are unstable it means your clusters are possibly not unique enough and you should reduce the number of clusters to get a more stable solution. How did you pick the number of clusters?

[HLuffy]

Thanks Reeza for he quick reply. I did choose the global peak value for estimation criterion and choose the number of cluster between 2 and 10 and the result give me 6 clusters. how I can now is my cluster are stable is there any way to know the number of iterations to find the stability? btw I choose the Euclidean distance for the similarity distance.

[Reeza]

I'm not aware of a stability measure (it may exist, just not aware) but it's pretty subject dependent as well I suspect.
For the # of clusters, did you look at the graphs and use the elbow method to determine the optimal # of clusters?
And just as an FYI stability isn't always possible in a clustering model and you'll almost never get 100% stability with real data.

[HLuffy]

the number was determined by ABC criterion. but my pb it's not in the number of the cluster but in the clusters they change after every repetition. is is the number of the cluster that cause that? I know that I can had 100 % stability but is there any heuristic rules or academics way after a certain percentage take decision about the stability?

[HLuffy]

here's a picture of selection # of clusters using ABC selection

[Reeza]

Sorry, not super familiar with the output of EM Miner for Clustering. I definitely cannot interpret a graph without axes, context or titles.

[HLuffy]

I updated the graph if that can help you to understand . ABC Statistics — displays the aligned box criterion statistics. The horizontal axis is the number of clusters and the vertical axis is the gap between the error measure from the reference data and the input data. The vertical line indicates the estimated number of clusters for the data.
Estimation Criterion — specifies the estimation criterion used in the aligned box criterion method. Global Peak Value uses the maximum peak value across all peak values in the gap statistics.

[Reeza]

Sorry, this is beyond my current recall for K-Means.

[HLuffy]

Thank you so much @Reeza !