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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 5 (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
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 3 (2 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.
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 1 (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.
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.