Threshold Validity for Mutual Neighborhood Clustering

Clustering algorithms have the annoying habit of finding clusters in random data. This note presents a theoretical analysis of the threshold of the mutual neighborhood clustering algorithm (MNCA) [l] under the hypothesis of random data. This yields a theoretical minimum value of this threshold below which even unclustered data is broken into separate clusters. To derive the threshold, a theorem about mutual near neighbors in a Poisson process is stated and proved. Simple experiments demonstrate the usefulness of the theoretical thresholds.