# How do you describe the clusters created by k-means?

I understand how the clustering algorithm k-means works and I can map any new point to any of the lusters using the predict function.

What I want to understand is: how can I describe the clusters?

For example, if I have three variables, x, y, and z, I would like to be able that, say, people in cluster 1 are those for which x is in between these values, unless y is that and then x is in between these other values, etc.

I understand that, if you have hundreds of variables, this becomes very difficult, is there some kind of "decision tree"-type of description I can use?

Alternatively, is there a way to output what the function kmeans derived by the algorithm, which I will use to predict any new point, looks like?

One thing you can use is the cluster_centers_ (it's an attribute from your trained KMeans).