Integrative Analysis of Dynamic Networks

Doctoral thesis, 2014

Networks play a central role in several disciplines such as computational biology, social network analysis, transportation planning and many others; and consequently, several methods have been developed for network analysis. However, in many cases, the study of a single network is insufficient to discover patterns with multiple facets and subtle signals. Integrative analysis is necessary in order to fuse weak information present in multiple networks into a more confident prediction, especially in domains where there are diverse modes of data acquisition e.g.~with modern biological technologies. This is further complicated by the fact that most real-world networks are inherently dynamic in nature. Discerning how networks evolve over time is crucial to unraveling the underlying phenomenon governing the system. Though network science has grown to include advances from diverse fields ranging from classical results in graph theory and approximation algorithms to newer methods focussed on study of real-world networks, integrative analysis of multiple dynamic networks is yet to be fully explored. This thesis makes two-fold contribution in this area. The first part of this thesis presents work aimed at integrative analysis of multiple networks reflecting the diverse relationships among a common set of actors or nodes. We make the connection between Lovasz theta function, a celebrated result in graph theory, and Kernel methods in machine learning. This allows us to develop new algorithms for classical graph-theoretic problems like planted clique recovery, graph coloring and max k-cut. We also present a new scalable method for discovering common dense subgraphs from multiple networks, with significant computational advantage over previous state-of-the-art enumerative approaches. Motivated by the SVM-theta connection, we design two new ``global'' graph kernels which can be used for graph classification. The kernels capture global graph properties like girth, while being competitive with existing ``local'' graph kernels. The second part of this thesis investigates the problem of learning time-varying interactions based on node observation data using the framework of probabilistic graphical models. We explore two facets of this problem: modelling the influence of gene function on dynamic gene-gene interactions; and, capturing higher-order time-varying networks in a transport application.