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So the K-means algorithm seems simple enough as I understand it: given some documents, turn those documents into points, initialize some number of k (centroids), assign document-points to nearest centroid, then iterate centroid positions until those centroids accurately identify k number of clusters.
Where document points: D = {d1, ... ,dN}

This is where I'm having some confusion. What are the values of D? are they just the document ids such that d1 is document 0, d2 is document 1, etc. If so, then how does one turn them into points?
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Are they points, such that d1 is (2,3), d2 is (1,1), etc. If so, how are those points determined? Are they supposed to be already known? Basically, what is D, and how do you know what the values of D are?

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As it turns out, I was wrong on both accounts. D is a document vector as defined by the Vector Space Model. Each dimension in D corresponds to a term such that for D = {5,10,15}, term 1 appears 5 times, term 2 appears 10 times, etc.

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