Unsupervised clustering with unknown number of clusters

Question

I have a large set of vectors in 3 dimensions. I need to cluster these based on Euclidean distance such that all the vectors in any particular cluster have a Euclidean dista

Answer 1

Check out the DBSCAN algorithm. It clusters based on local density of vectors, i.e. they must not be more than some ε distance apart, and can determine the number of clusters automatically. It also considers outliers, i.e. points with an unsufficient number of ε-neighbors, to not be part of a cluster. The Wikipedia page links to a few implementations.