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ADE4: a multivariate analysis and graphical display software
 Stat. Comput
, 1997
"... e searching, zooming, selection of points, and display of data values on factor maps. The user interface is simple and homogeneous among all the programs; this contributes to making the use of ADE4 very easy for nonspecialists in statistics, data analysis or computer science. Keywords: Multivar ..."
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Cited by 45 (8 self)
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e searching, zooming, selection of points, and display of data values on factor maps. The user interface is simple and homogeneous among all the programs; this contributes to making the use of ADE4 very easy for nonspecialists in statistics, data analysis or computer science. Keywords: Multivariate analysis, principal component analysis, correspondence analysis, instrumental variables, canonical correspondence analysis, partial least squares regression, coinertia analysis, graphics, multivariate graphics, interactive graphics, Macintosh, HyperCard, Windows 95 1. Introduction ADE4 is a multivariate analysis and graphical display software for Apple Macintosh and Windows 95 microcomputers. It is made up of several standalone applications, called modules, that feature a wide range of multivariate analysis methods, from simple onetable analysis to threeway table analysis and twotable coupling methods. It also provides many possibilitie
Graphtheoretic scagnostics
 In Proc. 2005 IEEE Symp. on Information Visualization (INFOVIS
, 2005
"... We introduce Tukey and Tukey scagnostics and develop graphtheoretic methods for implementing their procedure on large datasets. ..."
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Cited by 24 (0 self)
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We introduce Tukey and Tukey scagnostics and develop graphtheoretic methods for implementing their procedure on large datasets.
Corrgrams: Exploratory displays for correlation matrices
, 2002
"... Correlation and covariance matrices provide the basis for all classical multivariate techniques. ..."
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Cited by 23 (6 self)
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Correlation and covariance matrices provide the basis for all classical multivariate techniques.
The analysis of vegetationenvironment relationships by canonical correspondence analysis
, 1987
"... Canonical correspondence analysis (CCA) is introduced as a multivariate extension of weighted averaging ordination, which is a simple method for arranging species along environmental variables. CCA constructs those linear combinations of environmental variables, along which the distributions of the ..."
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Cited by 22 (1 self)
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Canonical correspondence analysis (CCA) is introduced as a multivariate extension of weighted averaging ordination, which is a simple method for arranging species along environmental variables. CCA constructs those linear combinations of environmental variables, along which the distributions of the species are maximally separated. The eigenvalues produced by CCA measure this separation. As its name suggests, CCA is also a correspondence analysis technique, but one in which the ordination axes are constrained to be linear combinations of environmental variables. The ordination diagram generated by CCA visualizes not only a pattern of community variation (as in standard ordination) but also the main features of the distributions of species along the environmental variables. Applications demonstrate that CCA can be used both for detecting speciesenvironment relations, and for investigating specific questions about the response of species to environmental variables. Questions in community ecology that have typically been studied by 'indirect ' gradient analysis (i.e. ordination followed by external interpretation of the axes) can now be answered more directly by CCA.
Milestones in the history of thematic cartography, statistical graphics, and data visualization
 13TH INTERNATIONAL CONFERENCE ON DATABASE AND EXPERT SYSTEMS APPLICATIONS (DEXA 2002), AIX EN PROVENCE
, 1995
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Two purposes for matrix factorization: A historical appraisal
 SIAM Review
"... Abstract. Matrix factorization in numerical linear algebra (NLA) typically serves the purpose of restating some given problem in such a way that it can be solved more readily; for example, one major application is in the solution of a linear system of equations. In contrast, within applied statistic ..."
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Cited by 18 (0 self)
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Abstract. Matrix factorization in numerical linear algebra (NLA) typically serves the purpose of restating some given problem in such a way that it can be solved more readily; for example, one major application is in the solution of a linear system of equations. In contrast, within applied statistics/psychometrics (AS/P), a much more common use for matrix factorization is in presenting, possibly spatially, the structure that may be inherent in a given data matrix obtained on a collection of objects observed over a set of variables. The actual components of a factorization are now of prime importance and not just as a mechanism for solving another problem. We review some connections between NLA and AS/P and their respective concerns with matrix factorization and the subsequent rank reduction of a matrix. We note in particular that several results available for many decades in AS/P were more recently (re)discovered in the NLA literature. Two other distinctions between NLA and AS/P are also discussed briefly: how a generalized singular value decomposition might be defined, and the differing uses for the (newer) methods of optimization based on cyclic or iterative projections.
A singularly valuable decomposition: The SVD of a matrix
 College Math Journal
, 1996
"... Every teacher of linear algebra should be familiar with the matrix singular value decomposition (or SVD). It has interesting and attractive algebraic properties, and conveys important geometrical and theoretical insights about linear transformations. The close connection between the SVD and the well ..."
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Cited by 14 (0 self)
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Every teacher of linear algebra should be familiar with the matrix singular value decomposition (or SVD). It has interesting and attractive algebraic properties, and conveys important geometrical and theoretical insights about linear transformations. The close connection between the SVD and the well known theory of diagonalization for symmetric matrices makes the topic immediately accessible to linear algebra teachers, and indeed, a natural extension of what these teachers already know. At the same time, the SVD has fundamental importance in several different applications of linear algebra. Strang was aware of these facts when he introduced the SVD in his now classical text [22, page 142], observing...it is not nearly as famous as it should be. Golub and Van Loan ascribe a central significance to the SVD in their definitive explication of numerical matrix methods [8, page xiv] stating...perhaps the most recurring theme in the book is the practical and theoretical value of [the SVD]. Additional evidence of the significance of the SVD is its central role in a number of papers in recent years in Mathematics Magazine and The American Mathematical Monthly (for example [2, 3, 17, 23]). Although it is probably not feasible to include the SVD in the first linear algebra course, it definitely deserves a place in more advanced undergraduate courses, particularly those with a numerical or applied emphasis. My primary goals in this article are to bring the topic to the attention of a broad audience,
Neural and Statistical Methods for the Visualization of Multidimensional Data
 DISSERTATION, KATEDRA METOD KOMPUTEROWYCH UMK
, 2001
"... In many fields of engineering science we have to deal with multivariate numerical data. In order to choose the technique that is best suited to a given task, it is necessary to get an insight into the data and to "understand" them. Much information allowing the understanding of multivariate data, th ..."
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Cited by 8 (2 self)
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In many fields of engineering science we have to deal with multivariate numerical data. In order to choose the technique that is best suited to a given task, it is necessary to get an insight into the data and to "understand" them. Much information allowing the understanding of multivariate data, that is the description of its global structure, the presence and shape of clusters or outliers, can be gained through data visualization. Multivariate data visualization can be realized through a reduction of the data dimensionality, which is often performed by mathematical and statistical tools that are well known. Such tools are Principal Components Analysis or Multidimensional Scaling. Artificial neural networks have developed and found applications mainly in the last two decades, and they are now considered as a mature field of research. This thesis investigates the use of existing algorithms as applied to multivariate data visualization. First an overview of existing neural and statistical techniques applied to data visualization is presented. Then a comparison is made between two chosen algorithms from the point of view of multivariate data visualization. The chosen neural network algorithm is Kohonen's SelfOrganizing Maps, and the statistical technique is Multidimensional Scaling. The advantages and drawbacks from the theoretical and practical viewpoints of both approaches are put into light. The preservation of data topology involved by those two mapping techniques is discussed. The multidimensional scaling method was analyzed in details, the importance of each parameter was determined, and the technique was implemented in metric and nonmetric versions. Improvements to the algorithm were proposed in order to increase the performance of the mapping process. A graphic...
Expression profile analysis of the lowoxygen response in Arabidopsis root cultures
 Plant Cell
, 2002
"... We used DNA microarray technology to identify genes involved in the lowoxygen response of Arabidopsis root cultures. A microarray containing 3500 cDNA clones was screened with cDNA samples taken at various times (0.5, 2, 4, and 20 h) after transfer to lowoxygen conditions. A package of statistical ..."
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Cited by 8 (0 self)
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We used DNA microarray technology to identify genes involved in the lowoxygen response of Arabidopsis root cultures. A microarray containing 3500 cDNA clones was screened with cDNA samples taken at various times (0.5, 2, 4, and 20 h) after transfer to lowoxygen conditions. A package of statistical tools identified 210 differentially expressed genes over the four time points. Principal component analysis showed the 0.5h response to contain a substantially different set of genes from those regulated differentially at the other three time points. The differentially expressed genes included the known anaerobic proteins as well as transcription factors, signal transduction components, and genes that encode enzymes of pathways not known previously to be involved in lowoxygen metabolism. We found that the regulatory regions of genes with a similar expression profile contained similar sequence motifs, suggesting the coordinated transcriptional control of groups of genes by common sets of regulatory factors.