Probability Models and Limit Theorems for Random Interval Graphs with Applications to Cluster Analysis

Assume that n k-dimensional data points have been obtained and subjected to a cluster analysis algorithm. A potential concern is whether the resulting clusters have a “causal” interpretation or whether they are merely consequences of a “random” fluctuation. In this report, the asymptotic properties of a number of potentially useful combinatorial tests based on the theory of random interval graphs are described. Some preliminary numerical results illustrating their possible application as a method of resolving the above question are provided.