Representing Big Data as Networks: New Methods and Insights.

Our world produces massive data every day; they exist in diverse forms, from pairwise data and matrix to time series and trajectories. Meanwhile, we have access to the versatile toolkit of network analysis. Networks also have different forms; from simple networks to higher-order network, each representation has different capabilities in carrying information. For researchers who want to leverage the power of the network toolkit, and apply it beyond networks data to sequential data, diffusion data, and many more, the question is: how to represent big data and networks? This dissertation makes a first step to answering the question. It proposes the higher-order network, which is a critical piece for representing higher-order interaction data; it introduces a scalable algorithm for building the network, and visualization tools for interactive exploration. Finally, it presents broad applications of the higher-order network in the real-world.