The objective of this collaborative research award is to establish a comprehensive knowledge-base for detecting low-diameter clusters in network models of social and biological big-data that are subject to measurement errors and incomplete information. This research study focuses on a novel model for detecting clusters in social and biological networks called a "k-club." Some key innovations pursued as part of this study include the use of a risk measure from financial engineering that is used to quantify losses in cluster cohesiveness that results from the measurement errors and uncertainty that underlies such network models of big data. This measure represents the downside risk of high losses in the worst-case scenarios leading to risk-averse mathematical models that facilitate the detection of clusters that are more likely to be application significant. The models and algorithms that result from this study will be validated using laboratory experimental data and expertise provided by collaborators in biological sciences, and also by using publicly available social and financial network datasets.
If successful, this work can enable biologists to better understand complex biological networks, accelerate discoveries and reduce experimental costs. The research has the potential to spur fundamental discoveries that can lead to advances in biomedicine, agriculture and bioenergy with positive societal impacts. High School mathematics teachers will be engaged to receive first-hand experience in large-scale network/data analysis as well as identify and transfer appropriate material to their classroom via active learning exercises. Enhancing minority participation and professional development are key outreach goals of this project. Graduate and undergraduate students from under-represented groups will be actively sought to become engaged in the research and hopefully the professoriate as recommended by the National Science Board and aligned with the America COMPETES Reauthorization Act.
