Say I have a dataset of n vectors. These are, by nature, clustered so that there is a significant distance difference between any two points within a cluster and any two points in separate clusters.
I want to create a single centroid per single cluster. However, I cannot initially know how many clusters there are - thus I cannot pre-define the k in K-means clustering.
What is the best way to define the k in K-Means, given the dense and clear clustering of the data?