Clustering and embedding based analysis of multilayer networks and hypergraphs to identify higher-order relationships and predict rare events

Project description

Entities in complex networks interact with each other through multiple pathways. Hypergraph modeling and multilayer networks provide improved techniques to capture these functional and structural features of real-world processes. Moreover, such network processes are highly characterized by stochasticity. The role of Markov chains and random walks could help to develop novel algorithms for detecting clusters, cliques, and motifs that help simplify our understanding of the system and potentially help us understand how to tweak the system efficiently to control it in a desirable manner. Sometimes accurately modeling the complex network data is not enough and we need to be able to predict interesting features for the individual units or clusters of the graphs. Being able to identify ground-truth clusters with high accuracy and then classify them into correctly labeled classes is a challenging problem that requires leveraging cutting-edge machine-learning algorithms to extract meaningful representations/embeddings from complex network structures to facilitate more effective analysis and prediction tasks. This would have applications in social network analysis as well as clustering for neural activity in the brain. Many efficient algorithms have been developed by the network science community but combining them in a novel manner to solve higher-order analysis and precision tasks has received relatively less attention. Moreover, real-world complex processes are also characterized by unexpected contingencies and in some cases catastrophic failures. Clustering and embedding algorithms for network data shall also be investigated for their effectiveness to detect such rare “black swan” events by incorporating simulation techniques and fat-tailed distributions, and then these shall be validated through case studies and application to real-world empirical as well as synthetic datasets.

Outcomes

The successful completion of this project will yield the following outcomes:
a) Develop a general modeling framework for complex processes and associated black swan events that allows us to detect anomalies, proactively identify potential bottlenecks, vulnerabilities, or inefficiencies
b) Develop techniques specifically tailored for multilayer networks and hypergraphs to enhance robustness against noise, missing data, and uncertainty.
c) Novel network embedding techniques capable of capturing complex structural and semantic information from networks.
d) Research publications in prestigious conferences and journals as well as open-source data and codes.

Essential capabilities

Mathematical maturity, algorithmic thinking, proficiency in Matlab, proficiency in LaTeX, experience with Python.

Desireable capabilities

Exposure to the theories of Markov Chains, Random Walks, and Network science.

Expected qualifications (Course/Degrees etc.)

B.Tech. or bachelor’s degree in mathematics or statistics. Master’s degrees in technology or engineering (MS or MTech) are also welcome.