I have a data set of points which are grouped into clusters like so:

![enter image description here](https://i.stack.imgur.com/SiPgI.png)

I'd like to use ArcGIS or Python to create a point layer of the centroids of each cluster but I can't seem to find the right tools. I looked into hot spot analysis but it doesn't seem to apply, since my features aren't numerically weighted. I also tried the Integrate tool with a reasonable tolerance but I didn't see any changes.