SPECTRUM-BASED AND COLLABORATIVE NETWORK TOPOLOGY ANALYSIS AND VISUALIZATION

Networks are of significant importance in many application domains, such as World Wide Web and social networks, which often embed rich topological information. Since network topology captures the organization of network nodes and links, studying net- work topology is very important to network analysis. In this dissertation, we study networks by analyzing their topology structure to explore community structure, the relationship among network members and links as well as their importance to the belonged communities. We provide new network visualization methods by studying network topology through two aspects: spectrum-based and collaborative visualiza- tion techniques. For the spectrum-based network visualization, we use eigenvalues and eigenvectors to express network topological features instead of using network datasets directly. We provide a visual analytics approach to analyze unsigned networks based on re- cent achievements on spectrum-based analysis techniques which utilize the features of node distribution and coordinates in the high dimensional spectral space. To assist the interactive exploration of network topologies, we have designed network visual- ization and interactive analysis methods allowing users to explore the global topology structure. Further, to address the question of real-life applications involving of both positive and negative relationships, we present a spectral analysis framework to study both signed and unsigned networks. Our framework concentrates on two problems of net- work analysis - what are the important spectral patterns and how to use them to study signed networks. Based on the framework, we present visual analysis methods, which guide the selection of k-dimensional spectral space and interactive exploration of network topology. With the increasing complexity and volume of dynamic networks, it is important to adopt strategies of joint decision-making through developing collaborative visualiza- tion approaches. Thus, we design and develop a collaborative detection mechanism with matrix visualization for complex intrusion detection applications. We establish a set of collaboration guidelines for team coordination with distributed visualization tools. We apply them to generate a prototype system with interactions that facilitates collaborative visual analysis. In order to evaluate the collaborative detection mechanism, a formal user study is presented. The user study monitored participants to collaborate under co-located and distributed collaboration environments to tackle the problems of intrusion detection. We have observed participants’ behaviors and collected their performances from the aspects of coordination and communication. Based on the results, we conclude several coordination strategies and summarize the values of communication for collaborative visualization. Our visualization methods have been demonstrated to be efficient topology explo- ration with both synthetic and real-life datasets in spectrum-based and collaborative exploration. We believe that our methods can provide useful information for future design and development of network topology visualization system

Future Challenges and Unsolved Problems in Multi-field Visualization

Evaluation, solved and unsolved problems, and future directions are popular themes pervading the visualization community over the last decade. The top unsolved problem in both scientific and information visualization was the subject of an IEEE Visualization Conference panel in 2004. The future of graphics hardware was another important topic of discussion the same year. The subject of how to evaluate visualization returned a few years later. Chris Johnson published a list of 10 top problems in scientific visualization research. This was followed up by report of both past achievements and future challenges in visualization research as well as financial support recommendations to the National Science Foundation (NSF) and National Institute of Health (NIH). Chen recently published the first list of top unsolved information visualization problems. Future research directions of topology-based visualization was also a major theme of a workshop on topology-based methods. Laramee and Kosara published a list of top future challenges in human-centered visualization

Topology Based Flow Analysis and Superposition Effects

Using topology for feature analysis in flow fields faces several problems. First of all, not all features can be detected using topology based methods. Second, while in flow feature analysis the user is interested in a quantification of feature parameters like position, size, shape, radial velocity and other parameters of feature models, many of these parameters can not be determined using topology based methods alone. Additionally, in some applications it is advantageous to regard the vector field as a superposition of several, possibly simple, features. As topology based methods are quite sensitive to superposition effects, their precision and usability is limited in these cases. In this paper, topology based analysis and visualization of flow fields is estimated and compared to other feature based approaches demonstrating these problems

Topological Machine Learning with Persistence Indicator Functions

Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional scaling, while providing a firm theoretical ground. Many modern machine learning algorithms, however, are based on kernels. This paper presents persistence indicator functions (PIFs), which summarize persistence diagrams, i.e., feature descriptors in topological data analysis. PIFs can be calculated and compared in linear time and have many beneficial properties, such as the availability of a kernel-based similarity measure. We demonstrate their usage in common data analysis scenarios, such as confidence set estimation and classification of complex structured data.Comment: Topology-based Methods in Visualization 201

Persistent Intersection Homology for the Analysis of Discrete Data

Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional manifold. In such cases, persistent homology can be successfully employed to extract features, remove noise, and compare data sets. The underlying problems in some application domains, however, turn out to represent multiple manifolds with different dimensions. Algebraic topology typically analyzes such problems using intersection homology, an extension of homology that is capable of handling configurations with singularities. In this paper, we describe how the persistent variant of intersection homology can be used to assist data analysis in visualization. We point out potential pitfalls in approximating data sets with singularities and give strategies for resolving them.Comment: Topology-based Methods in Visualization 201

HyperNetX: A Python package for modeling complex network data as hypergraphs

HyperNetX (HNX) is an open source Python library for the analysis and visualization of complex network data modeled as hypergraphs. Initially released in 2019, HNX facilitates exploratory data analysis of complex networks using algebraic topology, combinatorics, and generalized hypergraph and graph theoretical methods on structured data inputs. With its 2023 release, the library supports attaching metadata, numerical and categorical, to nodes (vertices) and hyperedges, as well as to node-hyperedge pairings (incidences). HNX has a customizable Matplotlib-based visualization module as well as HypernetX-Widget, its JavaScript addon for interactive exploration and visualization of hypergraphs within Jupyter Notebooks. Both packages are available on GitHub and PyPI. With a growing community of users and collaborators, HNX has become a preeminent tool for hypergraph analysis.Comment: 3 pages, 2 figure