A multivariate network is one where the nodes and/or edges are associated with attributes. This type of network is widespread, with examples including social networks, physical networks such as power grids, networks modeling cellular processes in biology, and trees describing evolutionary relationships between species. The need for visualizing MVNs arises when the structure (the topology) of the network needs to be analyzed together with the node or edge attributes. This presents a challenge when visualizing topology and attributes in the same view, since choosing efficient encodings for one aspect often interferes with the ability to effectively visualize the other. Our work contributes to the space of multivariate network visualization by first organizing the design space of MVN visualization techniques into a typology and identifying the limits of existing approaches. Given this landscape of techniques, we make two technique contributions: (1) an applied design study with domain experts which explores visualizing attributed genealogies, and (2) a general MVNV visualization approach that addresses the challenge of simultaneously visualizing topology and attributes well. We also contribute an empirical study which provides experimental evidence on the performance of the two most commonly used MVNV techniques: node-link diagrams and adjacency matrices. Finally, we reflect on the evaluation component of the completed work, including challenges and potential alternative approaches in future work. This body of work will provide guidance for practitioners, visualization researchers, and domain experts using MVNs for real-world exploration.

One of the challenges in data analysis is studying the behavior of a complex, non-linear systems, based on a large set of samples generated by computer simulations or a set of experiments on real-world physical phenomena. Analysis of the results can then be used to improve the models, find optimal solutions, uncover unknown relationships and support decision-making. Previous topology-based approaches segmented the parameter space using an approximate Morse-Smale complex on the cloud of point samples to support features extraction and segmentation, as well as generate simplified geometric summaries. However, these methods rely on the user to select an appropriate global refinement level of the hierarchy (persistence level) with minimal insight from the system.

In this presentation, I will describe a new framework that facilitate visual exploration and analysis of the space of all possible partitioning induced by the hierarchical Morse-Smale. Our approach is based on viewing the approximated Morse-Smale complex as a set of nested space partitions, fitting regression models in each partition and evaluating the fitness of these models. Moreover, different models and measures can be defined and evaluated on the fly as well as used to evaluate relative fitness between partitions are different levels of refinement. These in turn provide insights that help identify distinct space partitions, which exhibit unique behaviors of the output function with respect to the input parameters. The approach also introduces the notion of both non-uniform and non-consistent simplifications.