We use random geometric graphs to describe clusters of higher dimensional data points which are bijectively mapped to a (possibly) lower dimensional space where an equivalent random cluster model is used to calculate the expected number of modes to be found when separating the data of a multi-modal data set into distinct clusters. Furthermore, as a function of the expected number of modes and the number of data points in the sample, an upper bound on a given distance measure is found such that data points have the greatest correlation if their mutual distances from a common center is less than or equal to the calculated bound... (read more)

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