Data visualization through graph drawing
type: Item
instance of: scholarly article
title: Data visualization through graph drawing
zbMATH Open document ID: 1007.62003
author: George Michailidis
author: Jan De Leeuw
published in: Computational Statistics
publication date: 2003-03-09T00:00:00Z
full work available at URL: 1js880hs
review text: Let there be \(n\) objects \(v_i\), \(i=1,\dots,n\), and the adjacency matrix \(A=\{a_{ij}\}_{i,j=1}^n\) where \(a_{ij}\in\{0,1\}\), and \(a_{ij}=1\) means that \(v_i\) and \(v_j\) are adjacent (connected). The problem is to represent \(v_j\) by points \(z_j\in R^s\) such that \[ \sigma_\phi(Z)=\sum_{i,j=1}^n a_{ij}\phi(d(z_i,z_j))\to\min, \] where \(d\) is a distance in \(R^s\) (e.g., \(l_p\)-distance) and \(\phi\) is a fixed increasing function. A minimization algorithm is proposed in the case where \(\phi(d(z_i,z_j))\) is the squared \(l_2\)-distance. An iterative procedure using minimization of surrogate functions at each step is considered for more general cases. Applications to bipartite graphs and parallel coordinate plots are considered.
Mathematics Subject Classification ID: 62A09
Mathematics Subject Classification ID: 62H25
zbMATH DE Number: 1878623
zbMATH Keywords: majorization algorithm
zbMATH Keywords: multidimensional scaling
zbMATH Keywords: categorical multivariate data
MaRDI profile type: Publication
OpenAlex ID: W1579202901
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DOI: 10.1007/S001800100077
description: scientific article; zbMATH DE number 1878623