## Defining and calculating “closeness” between two vectors in a set

What's the best method for computing the "closeness" of two in a set of $N$-dimensional vectors with respect to the set itself? In other words, I have a collection of $N$-dimensional vectors and want to cluster the vectors that are "close" to one another. What is the best heuristic to do so?

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removed "group theory" tag – Yemon Choi Apr 30 2010 at 18:14
I think clustering is a fairly well studied problem in computer science. The Geomblog has a nice [series of posts](geomblog.blogspot.com/search/label/clustering) about it. What algorithm is best depends on the situation. – Omar Antolín-Camarena Apr 30 2010 at 19:59
Omar is right :) (I'm Geomblog !). If you provide more detail on what you want exactly, maybe we can suggest something. – Suresh Venkat May 1 2010 at 4:15