Visual Analysis of Sets of Heterogeneous Matrices Using Projection-Based Distance Functions and Semantic Zoom

• Published in: Computer graphics forum Vol. 33; no. 3; pp. 411 - 420
• Main Authors: Behrisch, Michael, Davey, James, Fischer, Fabian, Thonnard, Olivier, Schreck, Tobias, Keim, Daniel, Kohlhammer, Jörn
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.06.2014
• Subjects: Analysis; Categories and Subject Descriptors (according to ACM CCS); Computer networks; H.3.3 [Information Storage and Retrieval]: Information Search and Retrieval-Search process; Information processing; Mathematical analysis; Mathematical models; Monitors; Networks; Semantics; Studies; Visual; Visualization
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12397

Matrix visualization is an established technique in the analysis of relational data. It is applicable to large, dense networks, where node‐link representations may not be effective. Recently, domains have emerged in which the comparative analysis of sets of matrices of potentially varying size is relevant. For example, to monitor computer network traffic a dynamic set of hosts and their peer‐to‐peer connections on different ports must be analysed. A matrix visualization focused on the display of one matrix at a time cannot cope with this task. We address the research problem of the visual analysis of sets of matrices. We present a technique for comparing matrices of potentially varying size. Our approach considers the rows and/or columns of a matrix as the basic elements of the analysis. We project these vectors for pairs of matrices into a low‐dimensional space which is used as the reference to compare matrices and identify relationships among them. Bipartite graph matching is applied on the projected elements to compute a measure of distance. A key advantage of this measure is that it can be interpreted and manipulated as a visual distance function, and serves as a comprehensible basis for ranking, clustering and comparison in sets of matrices. We present an interactive system in which users may explore the matrix distances and understand potential differences in a set of matrices. A flexible semantic zoom mechanism enables users to navigate through sets of matrices and identify patterns at different levels of detail. We demonstrate the effectiveness of our approach through a case study and provide a technical evaluation to illustrate its strengths.