PhD Student, University of Minnesota
Nonlinear Models for Topology Inference and Learning over Graphs
Graphs are pervasive both in nature and engineered systems, often underlying the complex behavior observed in biological systems, microblogs and social interactions over the web, as well as global financial markets. Since their structures are often unobservable, in order to facilitate network analytics, one generally resorts to approaches capitalizing on measurable nodal processes to infer the unknown topology. Most contemporary graph topology inference approaches overwhelmingly rely on linear models due to their inherent simplicity and tractability, and presume that the nodal processes are directly observable.
Recognizing the limitations of linear models for modeling nonlinear phenomena, several variants of nonlinear models have recently emerged in several works. However, existing approaches mostly assume that the form of the nonlinear functions is known a priori, and develop algorithms to only estimate the unknown edge weights, which is a major limitation since such prior information may not be available in practice. Hence, in the present proposal, we will advocate nonlinear models to capture dependencies between observed nodal measurements, without explicit knowledge of the edge structure. Capitalizing on network properties such as edge sparsity, multi-layer structure, we further put forth a compressive suite of scalable algorithms for graph topology inference.
In addition to large-scale graphs, the massive development of connected devices and highly precise instruments has introduced the world to vast volumes of high-dimensional data, including images, videos, as well as time series generated from social, commercial and brain network interactions. Their efficient processing calls for dimensionality reduction techniques capable of properly compressing the data while preserving task-related characteristics, going beyond pairwise data correlations. Faced with these challenges, we put forth a broad nonlinear dimensionality reduction framework that accounts for data lying on known graphs (networks), and encompasses most of the existing dimensionality reduction methods as special cases. It is capable of capturing and preserving possibly nonlinear correlations that are ignored by linear methods, as well as taking into account information from multiple graphs.
Yanning Shen is a PhD student in the Department of Electrical and Computer Engineering at the University of Minnesota, Twin Cities. She’s working with the Signal Processing in Networking and Communications (SPiNCOM) group under the supervision of Prof. Georgios B. Giannakis. Her research interests include network science, online convex optimization, nonlinear modeling, with applications in social and biomedical networks. She was a receipt of SPS travel grant award in 2013 and 2017, and NSF travel grant award in 2016.