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A MaxentStress Model for Graph Layout
"... In some applications of graph visualization, input edges have associated target lengths. Dealing with these lengths is a challenge, especially for large graphs. Stress models are often employed in this situation. However, the traditional full stress model is not scalable due to its reliance on an in ..."
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Cited by 11 (3 self)
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In some applications of graph visualization, input edges have associated target lengths. Dealing with these lengths is a challenge, especially for large graphs. Stress models are often employed in this situation. However, the traditional full stress model is not scalable due to its reliance on an initial allpairs shortest path calculation. A number of fast approximation algorithms have been proposed. While they work well for some graphs, the results are less satisfactory on graphs of intrinsically high dimension, because nodes overlap unnecessarily. We propose a solution, called the maxentstress model, which applies the principle of maximum entropy to cope with the extra degrees of freedom. We describe a forceaugmented stress majorization algorithm that solves the maxentstress model. Numerical results show that the algorithm scales well, and provides acceptable layouts for large, nonrigid graphs. This also has potential applications to scalable algorithms for statistical multidimensional scaling (MDS) with variable distances.
More Flexible Radial Layout
"... We describe an algorithm for radial layout of undirected graphs, in which nodes are constrained to concentric circles centered at the origin. Such constraints are typical, e.g., in the layout of social networks, when structural centrality is mapped to geometric centrality or when the primary intenti ..."
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Cited by 8 (3 self)
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We describe an algorithm for radial layout of undirected graphs, in which nodes are constrained to concentric circles centered at the origin. Such constraints are typical, e.g., in the layout of social networks, when structural centrality is mapped to geometric centrality or when the primary intention of the layout is the display of the vicinity of a distinguished node. Our approach is based on an extension of stress minimization with a weighting scheme that gradually imposes radial constraints on the intermediate layout during the majorization process, and thus is an attempt to preserve as much information about the graph structure as possible. 1
Stress Functions for Nonlinear Dimension Reduction, Proximity Analysis, and Graph Drawing ∗
, 2012
"... Multidimensional scaling (MDS) is the art of reconstructing pointsets (embeddings) from pairwise distance data, and as such it is at the basis of several approaches to nonlinear dimension reduction and manifold learning. At present, MDS lacks a unifying methodology as it consists of a discrete colle ..."
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Cited by 2 (0 self)
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Multidimensional scaling (MDS) is the art of reconstructing pointsets (embeddings) from pairwise distance data, and as such it is at the basis of several approaches to nonlinear dimension reduction and manifold learning. At present, MDS lacks a unifying methodology as it consists of a discrete collection of proposals that differ in their optimization criteria, called “stress functions”. To correct this situation we propose (1) to embed many of the extant stress functions in a parametric family of stress functions, and (2) to replace the ad hoc choice among discrete proposals with a principled parameter selection method. This methodology yields the following benefits and problem solutions: (a) It provides guidance in tailoring stress functions to a given data situation, responding to the fact that no single stress function dominates all others across all data situations; (b) the methodology enriches the supply of available stress functions; (c) it helps our understanding of stress functions by replacing the comparison of discrete proposals with a characterization of the effect of parameters on embeddings; (d) it builds a bridge to graph drawing, which is the related but not identical art of constructing embeddings from graphs.
M.R.: On the Integration of Graph Exploration and Data Analysis: The Creative Exploration Toolkit
 Bisociative Knowledge Discovery. LNCS (LNAI
, 2012
"... Abstract. To enable discovery in large, heterogenious information networks a tool is needed that allows exploration in changing graph structures and integrates advanced graph mining methods in an interactive visualization framework. We present the Creative Exploration Toolkit (CET), which consists ..."
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Abstract. To enable discovery in large, heterogenious information networks a tool is needed that allows exploration in changing graph structures and integrates advanced graph mining methods in an interactive visualization framework. We present the Creative Exploration Toolkit (CET), which consists of a stateoftheart user interface for graph visualization designed towards explorative tasks and support tools for integration and communication with external data sources and mining tools, especially the datamining platform KNIME. All parts of the interface can be customized to fit the requirements of special tasks, including the use of node type dependent icons, highlighting of nodes and clusters. Through an evaluation we have shown the applicability of CET for structurebased analysis tasks. 1
CET: a tool for creative exploration of graphs
 Machine Learning and Knowledge Discovery in Databases
, 2010
"... Abstract. We present a tool for interactive exploration of graphs that integrates advanced graph mining methods in an interactive visualization framework. The tool enables efficient exploration and analysis of complex graph structures. For flexible integration of stateoftheart graph mining method ..."
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Abstract. We present a tool for interactive exploration of graphs that integrates advanced graph mining methods in an interactive visualization framework. The tool enables efficient exploration and analysis of complex graph structures. For flexible integration of stateoftheart graph mining methods, the viewer makes use of the open source data mining platform KNIME. In contrast to existing graph visualization interfaces, all parts of the interface can be dynamically changed to specific visualization requirements, including the use of node type dependent icons, methods for a marking if nodes or edges and highlighting and a fluent graph that allows for iterative growing, shrinking and abstraction of (sub)graphs. 1
Communicated by:
, 2012
"... We show that rectilinear graph drawing, the core problem of bendminimum orthogonal graph drawing, and uniform edgelength drawing, the core problem of forcedirected placement, are N Phard even for embedded paths if subjected to orthogonalordering constraints. Submitted: ..."
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We show that rectilinear graph drawing, the core problem of bendminimum orthogonal graph drawing, and uniform edgelength drawing, the core problem of forcedirected placement, are N Phard even for embedded paths if subjected to orthogonalordering constraints. Submitted:
LinkScope: Interactive Graph Analysis of Unstructured Text
"... This paper presents LinkScope, a toolkit for interactive analysis of text using node link graphs, with support for dynamic addition of attributes from tabular data. The interaction technique draws on ideas from 3D modeling, mesh deformation, and static graph drawing to promote discovery of hidden ..."
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This paper presents LinkScope, a toolkit for interactive analysis of text using node link graphs, with support for dynamic addition of attributes from tabular data. The interaction technique draws on ideas from 3D modeling, mesh deformation, and static graph drawing to promote discovery of hidden information across a wide variety of graph types and analysis tasks. The key innovation of this work is the application of methods traditionally reserved for automated graph layout and clustering, to produce useful taskspecific layout through dynamic interactions. Graph nodes are dynamically repositioned using an interpolated decay function over a single node movement provided by a user. We describe several variants of the interpolation method, including coupling it with a fast localcut algorithm for cluster selection. Compared to traditional layout mechanisms the technique is particularly useful when metadata nodes are added to a graph, increasing its connectivity. We show how the techniques can be used interactively to solve text analysis tasks including a case study on a collection of 16K awarded NSF grant proposals with metadata and a corpus of New York Times news articles.
Online Submission ID: 127 A MaxentStress Model for Graph Layout
"... In some applications of graph visualization, input edges have associated target lengths. Dealing with these lengths is a challenge, especially for large graphs. Stress models are often employed in this situation. However, the traditional full stress model is not scalable due to its reliance on an in ..."
Abstract
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In some applications of graph visualization, input edges have associated target lengths. Dealing with these lengths is a challenge, especially for large graphs. Stress models are often employed in this situation. However, the traditional full stress model is not scalable due to its reliance on an initial allpairs shortest path calculation. A number of fast approximation algorithms have been proposed. While they work well for some graphs, the results are less satisfactory on graphs of intrinsically high dimension, because nodes overlap unnecessarily. We propose a solution, called the maxentstress model, which applies the principle of maximum entropy to cope with the extra degrees of freedom. We describe a forceaugmented stress majorization algorithm that solves the maxentstress model. Numerical results 1 show that the algorithm scales well, and provides acceptable layouts for large, nonrigid graphs. This also has potential applications to scalable algorithms for statistical multidimensional scaling (MDS) with variable distances.