# what could this mean if your "elbow curve" looks like this?

This is from running kmeans clustering with k on the x-axis (ranging from 2 to 10) and the silhouette distance on the y-axis.

Clearly there's peaks at k=3, k=4 and it seems to decline from there. It doesn't resemble an elbow and thought it should rise as k gets larger (due to over fitting on he training set). Do I just lack data?

I'm computing the silhouette distance using a 80-20 train test split.

• So, what’s the size of your data? Apr 8 '19 at 20:46
• few thousand rows , TFIDF based clustering ~ 50 000 features
– MrL
Apr 8 '19 at 21:59

First of all, you do have two elbows: one at $$k=4$$ and a large one at $$k=8$$. The second isn't very apparent because you haven't drawn out the plot for larger values of $$k$$. If you do you might get a figure like this:
Secondly, you aren't meant to look for an elbow when computing the silhouette score! The silhouette score accounts for both inter- and intra-cluster distance, as such it can be used for selecting $$k$$ on its own (i.e. select the $$k$$ that produces the best silhouette score).
The "elbow" criterion should be used when dealing with metrics that tend to improve as $$k$$ increases (e.g. inertia).