Project web site for NSF grant IIS-1814931 (Link to NSF award site)
|| Project title:
|| III: Small: Collaborative Research: Network analysis and anomaly detection via global curvatures
|| Bhaskar DasGupta
|| Collaborative PI:
|| Réka Albert (Pennsylvania State University)
Curvatures of geometric shapes and topological spaces
in higher dimension are natural and powerful
generalizations of their simpler counter-parts, in
planes and other two-dimensional spaces, to higher
dimensions and play a fundamental role in physics,
mathematics and many other areas. In this collaborative
interdisciplinary proposal involving one investigator
each from the University of Illinois at Chicago and
the Pennsylvania State University, the investigators
will use powerful higher-dimensional curvature analysis
methods to provide the foundations of systematic and
computationally efficient approaches to find critical
components, measure redundancies and detect anomaly in
biological and social networks. There is a pressing need
for this, as identification of critical components are
crucial to the analysis of networks, and curvature-based
analysis methods provide a principled way of satisfying
this need using a systematic and rigorous theoretical
framework to achieve a clear understanding. The proposed
research will leverage further development of novel
combinatorial tools previously developed by the investigators,
in addition to developing new algorithmic and approximability
techniques. The algorithms developed in the course of this
project will be implemented for validation on simulated and
real data and will lead to open-source software for the
relevant research communities. In addition to substantial
impacts in network analysis, the proposed research will have
strong impacts on many other research areas in computational
biology, neuroscience and social network analysis. Other
broader impacts will include integration of research and
education via course and curriculum development, involvement
of undergraduates, minorities and under-represented groups,
effective dissemination of research, mentoring of undergraduate
and graduate students, outreach and community involvement, and
promoting diversity in related research and educational
activities. The two investigators have a proven track record of
extremely successful past collaboration via joint research
publications and grants and are therefore confident that this
grant will extend their past successful collaboration.
To achieve the goals of this project, the investigators will
explore two notions of curvature, namely Gromov-hyperbolic
curvature based on the properties of geodesics and higher-order
connectivities, and geometric curvatures based on identifying
networks with geometric complexes and using combinatorialization
of Ricci type curvatures. These curvature measures depend on
non-trivial global properties, such as distributions of geodesics
and higher-order correlations among nodes, of the given network
as opposed to many other measures that are local in nature.
The investigators will use these notions to identify non-trivial
critical components of the network whose removal affects the
change the network topology or dynamics in a significant manner.
The investigators will formulate mathematically precise
computational problems, study their properties, use novel
algorithmic tools to design efficient algorithms, and implement
the resulting algorithms to test their accuracy and efficiency.
The complementary backgrounds of the two investigators, namely
combinatorial optimization in computer science and computational
biology (DasGupta) and modelling and analysis of biological and
social networks (Albert), will make the two investigators a
perfect team for the interdisciplinary applications in this proposal.
Bhaskar DasGupta, Elena Grigorescu and Tamalika Mukherjee, On Locally Computing the Ollivier-Ricci Curvature of Graphs, 2022.
Tanima Chatterjee, Réka Albert, Stuti Thapliyal, Nazanin Azarhooshang and Bhaskar DasGupta, Detecting Network Anomalies Using Forman-Ricci Curvature and A Case Study for Human Brain Networks, (Nature) Scientific Reports, 11, 8121, 2021.
- Tanima Chatterjee, Bhaskar DasGupta and Réka Albert, A review of two network curvature measures, in Nonlinear Analysis and Global Optimization, Th. M. Rassias, and P. M. Pardalos (eds.), Springer Optimization and Its Applications series 167, 51-69, Springer, 2021.
Nazanin Azarhooshang, Prithviraj Sengupta and Bhaskar DasGupta, A Review of and Some Results for Ollivier-Ricci Network Curvature, Mathematics, 8, 1416, 2020.
- Bhaskar DasGupta, Mano Vikash Janardhanan and Farzane Yahyanejad, How did the shape of your network change? (On detecting network anomalies via non-local curvatures), Algorithmica, 82(7), 1741-1783, 2020.
- Farzane Yahyanejad, Bhaskar DasGupta and Réka Albert, A survey of some tensor analysis techniques for biological systems, Quantitative Biology, 7(4), 266-277, 2019.
- Bhaskar DasGupta, Topological implications of negative curvature for biological networks, 2018 IEEE 8th International Conference on Computational Advances in Bio and Medical Sciences (ICCABS 2018), p. 54, ©IEEE, 2018.
Publication related software
Collaborating researchers (outside UIC)
Pennsylvania State University (Collaborative PI)
Graduate students (Past and Present)