Joshua Neil

Publication Date



Identifying anomalies in computer networks is a challenging and complex problem. Often, anomalies occur in extremely local areas of the network. Locality is complex in this setting, since we have an underlying graph structure. To identify local anomalies, we introduce a scan statistic for data extracted from the edges of a graph over time. In the computer network setting, the data on these edges are multivariate measures of the communications between two distinct machines, over time. We describe two shapes for capturing locality in the graph: the star and the k-path. While the star shape is not new to the literature, the path shape, when used as a scan window, appears to be novel. Both of these shapes are motivated by hacker behaviors observed in real attacks. A hacker who is using a single central machine to examine other machines creates a star-shaped anomaly on the edges emanating from the central node. Paths represent traversal of a hacker through a network, using a set of machines in sequence. To identify local anomalies, these shapes are enumerated over the entire graph, over a set of sliding time windows. Local statistics in each window are compared with their historic behavior to capture anomalies within the window. These local statistics are model-based. To capture the communications between computers, we have applied two different models, observed and hidden Markov models, to each edge in the network. These models have been effective in handling various aspects of this type of data, but do not completely describe the data. Therefore, we also present ongoing work in the modeling of host-to-host communications in a computer network. Data speeds on larger networks require online detection to be nimble. We describe a full anomaly detection system, which has been applied to a corporate sized network and achieves better than real-time analysis speed. We present results on simulated data whose parameters were estimated from real network data. In addition, we present a result from our analysis of a real, corporate-sized network data set. These results are very encouraging, since the detection corresponded to exactly the type of behavior we hope to detect.

Degree Name


Level of Degree


Department Name

Mathematics & Statistics

First Committee Member (Chair)

Curtis B. Storlie

Second Committee Member

Scott Vander Weil

Third Committee Member

Terran Lane

Fourth Committee Member

Ronald Christensen

Project Sponsors

Los Alamos National Laboratory




Computer networks--Security measures--Statistical methods, Computer networks--Monitoring--Statistical methods, Computer security--Statistical methods.

Document Type