Finding Natural Clusters

On being presented with a set of points plotted on a plane space, most observers will agree that the set contains clusters of points if the distribution of the points meets certain conditions. We postulate that these conditions are: (1) that there are continuous, relatively densely populated regions of the space, and (2) that these are surrounded by continuous, relatively empty regions of the space. Using this definition for natural clusters we developed an algorithm for finding such clusters from the relative interpoint distances within a set. Starting with the closest pair of points, additional cluster members are sought by a minimum stepping stone strategy and accepted or rejected on the basis of parameters which indicate a discontinuity of closeness (i.e. a continuous, relatively empty space surrounding the points already admitted to the cluster) The procedure is repeated at a number of levels of resolution to give an overall view of the population. The resolution levels appropriate for a given set of points are determined from an analysis of the interpoint distances. Since the procedure uses only the relative distances between the points, it can be applied to points specified in any number of dimensions.