# Clustering mixed data: Find optimal number of clusters

What do you say about this plot to find the number of cluster for kmean or kproto for mixed data. Where is the elbow to identify? I would say 5? I have 11 feautures.

• the "elbow method" and silhouette analysis are two different concepts, check e.g. en.wikipedia.org/wiki/…
– oW_
Commented Nov 20, 2017 at 21:20

The bumps at 8 and 11 are likely just due to random initialization, and if you rerun with a different random seed, then they will be at a different k.

The elbow argument would probably suggest 3, but it is all but clear. I don't think there is a clear cut, but the values only drop as they would on uniform data.

So most likely, a) your distance function is not good enough, 2) the algorithm does not work on this data, and/or c) this evaluation does not work on this data.

You should select 9 as you can see from plot that for the WSS value there is a dip.

It doesn’t matter if you have 2 features or 9 features or n features. Clustering is on Data present in those features(it might depend on the amount of data).

• I have a little bit problem to validate such findings. Is it really better to use 11 than 8 where also is a dip? When I run multiple times cluster centers look different every time, so it is hard to Analyse the characteristics within each cluster. Any tips ?
– Tido
Commented Nov 21, 2017 at 7:48
• Uhm, high is bad. So 11 was worse than both 10 and 12... are you trying to make him pick the worst k? Commented Nov 21, 2017 at 7:52
• @Anony-Mousse what other method can you suggest?
– Tido
Commented Nov 21, 2017 at 8:34
• Can you do conclusion about cluster tendency from multiple correspondence analysis? Wenn MCA gives also about 10 dimensions to give 80% of variances it is a hint that you need so many clusters? With 3 dimensions only 20% variance can be explained. So 3 clusters are actually not good enough?
– Tido
Commented Nov 21, 2017 at 8:37
• "3 dimensions [...] variance explained" is PCA (meaningful only for continuous variables!), not clustering. You mix up things. Also, forget "clustering tendency". That is a synonym for "not uniform distributed". Starting looking at your data. Commented Nov 21, 2017 at 15:42