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

Behrisch, Michael and Davey, James and Fischer, Fabian and Thonnard, Olivier and Schreck, Tobias and Keim, Daniel A. and Kohlhammer, Jörn (2014):
Visual Analysis of Sets of Heterogeneous Matrices Using Projection-Based Distance Functions and Semantic Zoom.
In: Computer Graphics Forum, pp. 411-420, 33, (3), DOI: 10.1111/cgf.12397, [Article]

Abstract

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.

Item Type: Article
Erschienen: 2014
Creators: Behrisch, Michael and Davey, James and Fischer, Fabian and Thonnard, Olivier and Schreck, Tobias and Keim, Daniel A. and Kohlhammer, Jörn
Title: Visual Analysis of Sets of Heterogeneous Matrices Using Projection-Based Distance Functions and Semantic Zoom
Language: English
Abstract:

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.

Journal or Publication Title: Computer Graphics Forum
Volume: 33
Number: 3
Uncontrolled Keywords: Business Field: Visual decision support, Research Area: Human computer interaction (HCI), Information visualization, Visual analytics, Matrix representation, Similarity measures
Divisions: 20 Department of Computer Science
20 Department of Computer Science > Interactive Graphics Systems
Date Deposited: 12 Nov 2018 11:16
DOI: 10.1111/cgf.12397
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