Computed statistics indicating a node's position in a network have long been an important part of network analysis. Nearly as long, researchers have been concerned about the sensitivity of these computed statistics to unreliable or incomplete data. Recently, a number of studies have attempted to quantify these concerns through various simulations, however, these studies make several simplifying assumptions that are inappropriate for real network data. In particular, they assume that uncertainty/variability is equal for all nodes and edges in the network, despite evidence to the contrary. I have examined empirical networks as well as frequently used statistical models, with both indicating high variability for statistics related to weak ties (e.g. betweenness centrality) as well as low variability for statistics related to strong ties (e.g. closeness centrality).
Frequently, social network data originates in some (electronic) record of a specific social action. Despite this, there are few viable continuous-time models for representing the various ways in which social actions propagate through a social network. Specifically, the p* models generally require discrete observations of the entire network, while Siena models generally do not scale beyond tens to hundreds of nodes. Furthermore, these models have been developed to model the relatively stable patterns of social relationships, rather than the often fleeting specific social actions which contribute to their maintenance.
I have developed a variation on the Hawkes self-exciting process that I believe to be uniquely appropriate for the modeling of dynamic social activity. In particular, I have developed a parameterization that permits an intuitive causal interpretation in conjunction with a scalable algorithm for parameter estimation.
So far I've analyzed drug seizure networks, shipping networks, organizational network of terrorist groups, epidemiological networks and simulated social networks. Most of this analysis has been to test new methodologies I've developed. There are two main techniques I've been working on, manipulating network scale and aggregation and visualizing spatial dependencies in network topology.
There is a fundamental discord between network and space. Space is continuous; relationships in networks are defined as between discrete entities. This means that some level of aggregation of space (implicit or explicit) us required in order to do a meaningful analysis of the network. Different levels of aggregation can lead do quite different networks. I've been working on methods of capturing the tradeoffs of aggregation versus precision.
Second, visualization of social networks has been important historically in providing the intuition for many commonly used network statistics. My hope is that the visualization of spatially embedded network data will be similarly useful. However, simple visualizations of spatially embedded networks quickly become noisy and difficult to interpret. For this reason, I'm developing techniques for visualizing higher-level network topological properties and their interaction with spatial location. I am also working to develop a statistical measure of the spatial dependencies in structural properties of a spatially embedded network.
All of these techniques and more have been implemented in the Geospatial Network Visualizer in the ORA dynamic network analysis tool.
As an undergraduate I worked on two computer science-related projects. The first, working with Amy Csizmar Dalal, involved predicting the User-Perceived Quality of streaming multimedia clips. We gathered real-time metrics about the stream and used a simple nearest-neighbor regression to predict quality. I tested several different time-series distance metrics and developed a new metric.
I also worked with Dave Musicant on EnChIlADA:Environmental Chemistry through Intelligent Analysis of Data. We developed tools to aid environmental chemists in the analysis of Aerosol Time-of-Flight Mass Spectrometry data. We implemented a variety of clustering algorithms and distance metrics and tested them for real-world meaning and usefulness.
You can find my cv here.