On The Sharp Threshold Interval Length of Partially Connected Random   Geometric Graphs During K-Means Classification
  In $K$-means classification, a set of data will form clusters, i.e. classes, if the measured distances between data points (or some common point in each class) are below a certain threshold. With the assumption that the data points are randomly generated throughout some bounded region according to a certain probability distribution, we estimate the mean number of classes to form with high probability. 
Robert A. Murphy
math.PR