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Understanding Biplots
By: John Gower , Sugnet Gardner Gardner LubbeeBook Publisher: John Wiley & Sons
Imprint: Wiley
Format: ePub Encrypted (DRM)
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Biplots are a graphical method for simultaneously displaying two kinds of information; typically, the variables and sample units described by a multivariate data matrix or the items labelling the rows and columns of a two-way table. This book aims to popularize what is now seen to be a useful and reliable method for the visualization of multidimensional data associated with, for example, principal component analysis, canonical variate analysis, multidimensional scaling, multiplicative interaction and various types of correspondence analysis. Understanding Biplots: • Introduces theory and techniques which can be applied to problems from a variety of areas, including ecology, biostatistics, finance, demography and other social sciences. • Provides novel techniques for the visualization of multidimensional data and includes data mining techniques. • Uses applications from many fields including finance, biostatistics, ecology, demography. • Looks at dealing with large data sets as well as smaller ones. • Includes colour images, illustrating the graphical capabilities of the methods. • Is supported by a Website featuring R code and datasets. Researchers, practitioners and postgraduate students of statistics and the applied sciences will find this book a useful introduction to the possibilities of presenting data in informative ways.
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| Title of eBook: Understanding Biplots | |
| Release Date: 02-23-2011 | |
| Publisher: Wiley |
This eBook download is available in the following formats:
| Parent title | Understanding Biplots |
|---|---|
| Encrypted (DRM) | Yes |
| SKU | 9780470973202 |
| File size | 5809 |
| Security | n/a |
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| Read aloud | No Sys requirements Download reader |
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| Note | Excellent navigation features are available via Adobe such as bookmarks and a quick access table of contents. Text search is easily accessible. An Adobe DRM-protected file is different than a pdf file in that it uses Adobe DRM (Digital Rights Management) technology, which authors and publishers use to protect their content from illegal online distribution and to set certain privileges such as restrictions on copying and printing. |
Understanding Biplots
Chapter One
Introduction
Biplots have been with us at least since Descartes, if not from the time of Ptolemy who had a method for fixing the map positions of cities in the ancient world. The essential ingredients are coordinate axes that give the positions of points. From the very beginning, the concept of distance was central to the Cartesian system, a point being fixed according to its distance from two orthogonal axes; distance remains central to much of what follows. Descartes was concerned with how the points moved in a smooth way as parameters changed, so describing straight lines, conics and so on. In statistics, we are interested also in isolated points presented in the form of a scatter diagram where, typically, the coordinate axes represent variables and the points represent samples or cases. Cartesian geometry soon developed three-dimensional and then multidimensional forms in which there are many coordinate axes. Although two-dimensional scatter diagrams are invaluable for showing data, multidimensional scatter diagrams are not. Therefore, statisticians have developed methods for approximating multidimensional scatter in two, or perhaps three, dimensions. It turns out that the original coordinate axes can also be displayed as part of the approximation, although inevitably they lose their orthogonality. The essential property of all biplots is the two modes, such as variables and samples. For obvious reasons, we shall be concerned mainly with two-dimensional approximations but should stress at the outset that the bi- of biplots refers to the two modes and not the usual two dimensions used for display.
Biplots, not necessarily ref
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