A Test for Detecting Changes in Closed Networks Based on the Number of Communications Between Nodes

Authors

Christopher S. Wichman, University of Nebraska-LincolnFollow

Date of this Version

7-2013

Citation

C. S. Wichman, A Test for Detecting Changes in Closed Networks Based on the Number of Communications Between Nodes. Ph.D. dissertation, University of Nebraska-Lincoln, July 2013.

Comments

A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Statistics, Under the Supervision of Professor David B. Marx. Lincoln, Nebraska: July, 2013

Copyright (c) 2013 Christopher S. Wichman

Abstract

This dissertation presents a formal method for detecting changes in a closed communications network based on an “abnormal” shift in the number of communications between some of the nodes. The method relies on the analyst’s ability to define the network of interest; capture the number of communications between nodes; and to establish a history of normal communications flow between nodes over fixed intervals of time. A metric multi-dimensional scaling technique is then used to represent the network at each time interval with a k-dimensional (k = 1, 2, …) configuration. The affine bi-dimensional regression coefficient of determination (aR²) between all adjacent time periods is calculated and recorded. As time progresses, the configuration and aR² are found and compared to the historical aR²’s. When a time period’s aR² is abnormally low relative to the history, a change in the number of communications has been detected.

A simulation study was conducted using a closed network made up of ten nodes and three different edge density values (low, moderate, and high) to randomly generate the edges (connections) between nodes. A Poisson AR(1) process was used to generate the number of communications between nodes at each time period. Changes were then randomly assigned in time periods 26 and 52, and the aR²’s calculated between adjacent time periods. A separate simulation was conducted for each combination of edge density (3 levels), AR(1) correlation parameter (3 levels), number of edges perturbed (3 levels), perturbation factor (3 levels), time period of perturbation (2 levels), and configuration dimension (2 levels). The results suggest that under these conditions the method as proposed has reasonable power for detecting “abnormal” changes in the number of communications.

Adviser: David B. Marx