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E-raamat: Understanding Biplots

(University of Stellenbosch, South Africa), (University of Cape Town, South Africa), (Open University, UK)
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 23-Feb-2011
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781119972907
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Understanding BiplotsSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 23-Feb-2011
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781119972907
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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.

Arvustused

It is a monograph rather than a textbook, but individual chapters could very well be incorporated in a course on statistics.  (Mathematical Reviews Clippings, 1 January 2013)

 

 

 

Preface xi
1 Introduction
7(4)
1.1 Types of biplots
2(3)
1.2 Overview of the book
5(2)
1.3 Software
7(1)
1.4 Notation
7(4)
1.4.1 Acronyms
9(2)
2 Biplot basics
11(56)
2.1 A simple example revisited
11(3)
2.2 The biplot as a multidimensional scatterplot
14(6)
2.3 Calibrated biplot axes
20(12)
2.3.1 Lambda scaling
24(8)
2.4 Refining the biplot display
32(4)
2.5 Scaling the data
36(1)
2.6 A closer look at biplot axes
37(7)
2.7 Adding new variables: the regression method
44(3)
2.8 Biplots and large data sets
47(3)
2.9 Enclosing a configuration of sample points
50(14)
2.9.1 Spanning ellipse
53(1)
2.9.2 Concentration ellipse
54(3)
2.9.3 Convex hull
57(1)
2.9.4 Bagplot
58(4)
2.9.5 Bivariate density plots
62(2)
2.10 Buying by mail order catalogue data set revisited
64(2)
2.11 Summary
66(1)
3 Principal component analysis biplots
67(78)
3.1 An example: risk management
67(4)
3.2 Understanding PCA and constructing its biplot
71(9)
3.2.1 Representation of sample points
72(2)
3.2.2 Interpolation biplot axes
74(3)
3.2.3 Prediction biplot axes
77(3)
3.3 Measures of fit for PCA biplots
80(14)
3.4 Predictivities of newly interpolated samples
94(4)
3.5 Adding new axes to a PCA biplot and defining their predictivities
98(5)
3.6 Scaling the data in a PCA biplot
103(4)
3.7 Functions for constructing a PCA biplot
107(12)
3.7.1 Function PCAbipl
107(8)
3.7.2 Function PCAbipl.zoom
115(1)
3.7.3 Function PCAbipl.density
115(1)
3.7.4 Function PCAbipl.density.zoom
116(1)
3.7.5 Function PCA.predictivities
117(1)
3.7.6 Function PCA.predictions.mat
117(1)
3.7.7 Function vector.sum.interp
117(1)
3.7.8 Function circle.projection.interactive
118(1)
3.7.9 Utility functions
118(1)
3.8 Some novel applications and enhancements of PCA biplots
119(25)
3.8.1 Risk management example revisited
119(4)
3.8.2 Quality as a multidimensional process
123(5)
3.8.3 Using axis predictivities in biplots
128(1)
3.8.4 One-dimensional PCA biplots
128(7)
3.8.5 Three-dimensional PCA biplots
135(3)
3.8.6 Changing the scaffolding axes in conventional two-dimensional PCA biplots
138(1)
3.8.7 Alpha-bags, kappa-ellipses, density surfaces and zooming
139(1)
3.8.8 Predictions by circle projection
139(5)
3.9 Conclusion
144(1)
4 Canonical variate analysis biplots
145(60)
4.1 An example: revisiting the Ocotea data
145(8)
4.2 Understanding CVA and constructing its biplot
153(4)
4.3 Geometric interpretation of the transformation to the canonical space
157(3)
4.4 CVA biplot axes
160(2)
4.4.1 Biplot axes for interpolation
160(1)
4.4.2 Biplot axes for prediction
160(2)
4.5 Adding new points and variables to a CVA biplot
162(1)
4.5.1 Adding new sample points
162(1)
4.5.2 Adding new variables
162(1)
4.6 Measures of fit for CVA biplots
163(6)
4.6.1 Predictivities of new samples and variables
168(1)
4.7 Functions for constructing a CVA biplot
169(3)
4.7.1 Function CVAbipl
169(1)
4.7.2 Function CVAbipl.zoom
170(1)
4.7.3 Function CVAbipl.density
170(1)
4.7.4 Function CVAbipl.density.zoom
170(1)
4.7.5 Function CVAbipl.pred. regions
170(1)
4.7.6 Function CVA.predictivities
171(1)
4.7.7 Function CVA.predictions.mat
172(1)
4.8 Continuing the Ocotea example
172(6)
4.9 CVA biplots for two classes
178(7)
4.9.1 An example of two-class CVA biplots
178(7)
4.10 A five-class CVA biplot example
185(4)
4.11 Overlap in two-dimensional biplots
189(16)
4.11.1 Describing the structure of overlap
189(2)
4.11.2 Quantifying overlap
191(14)
5 Multidimensional scaling and nonlinear biplots
205(50)
5.1 Introduction
205(1)
5.2 The regression method
206(2)
5.3 Nonlinear biplots
208(4)
5.4 Providing nonlinear biplot axes for variables
212(15)
5.4.1 Interpolation biplot axes
215(3)
5.4.2 Prediction biplot axes
218(2)
5.4.2.1 Normal projection
220(2)
5.4.2.2 Circular projection
222(4)
5.4.2.3 Back-projection
226(1)
5.5 A PCA biplot as a nonlinear biplot
227(2)
5.6 Constructing nonlinear biplots
229(5)
5.6.1 Function Nonlinbipl
230(3)
5.6.2 Function CircularNonLinear.predictions
233(1)
5.7 Examples
234(9)
5.7.1 A PCA biplot as a nonlinear biplot
234(2)
5.7.2 Nonlinear interpolative biplot
236(1)
5.7.3 Interpolating a new point into a nonlinear biplot
237(1)
5.7.4 Nonlinear predictive biplot with Clark's distance
237(5)
5.7.5 Nonlinear predictive biplot with square root of Manhattan distance
242(1)
5.8 Analysis of distance
243(10)
5.8.1 Proof of centroid property for interpolated points in AoD
249(1)
5.8.2 A simple example of analysis of distance
250(3)
5.9 Functions AODplot and PermutationAnova
253(2)
5.9.1 Function AODplot
253(1)
5.9.2 Function PermutationAnova
254(1)
6 Two-way tables: biadditive biplots
255(34)
6.1 Introduction
255(1)
6.2 A biadditive model
256(1)
6.3 Statistical analysis of the biadditive model
256(4)
6.4 Biplots associated with biadditive models
260(1)
6.5 Interpolating new rows or columns
261(1)
6.6 Functions for constructing biadditive biplots
262(5)
6.6.1 Function biadbipl
262(3)
6.6.2 Function biad.predictivities
265(2)
6.6.3 Function biad.ss
267(1)
6.7 Examples of biadditive biplots: the wheat data
267(16)
6.8 Diagnostic biplots
283(6)
7 Two-way tables: biplots associated with correspondence analysis
289(76)
7.1 Introduction
289(1)
7.2 The correspondence analysis biplot
290(12)
7.2.1 Approximation to Pearson's chi-squared
290(1)
7.2.2 Approximating the deviations from independence
291(1)
7.2.3 Approximation to the contingency ratio
292(1)
7.2.4 Approximation to chi-squared distance
293(3)
7.2.5 Canonical correlation approximation
296(2)
7.2.6 Approximating the row profiles
298(1)
7.2.7 Analysis of variance and generalities
299(3)
7.3 Interpolation of new (supplementary) points in CA biplots
302(1)
7.4 Other CA related methods
303(3)
7.5 Functions for constructing CA biplots
306(6)
7.5.1 Function cabipl
306(4)
7.5.2 Function ca.predictivities
310(1)
7.5.3 Function ca. predictions.mat
310(1)
7.5.4 Functions indicatormat. construct.df.Chisq.dist
311(1)
7.5.5 Function cabipl.doubling
312(1)
7.6 Examples
312(42)
7.6.1 The RSA crime data set
312(33)
7.6.2 Ordinary PCA biplot of the weighted deviations matrix
345(1)
7.6.3 Doubling in a CA biplot
346(8)
7.7 Conclusion
354(11)
8 Multiple correspondence analysis
365(40)
8.1 Introduction
365(1)
8.2 Multiple correspondence analysis of the indicator matrix
366(6)
8.3 The Burt matrix
372(4)
8.4 Similarity matrices and the extended matching coefficient
376(1)
8.5 Category-level points
377(1)
8.6 Homogeneity analysis
378(3)
8.7 Correlational approach
381(2)
8.8 Categorical (nonlinear) principal component analysis
383(3)
8.9 Functions for constructing MCA related biplots
386(8)
8.9.1 Function cabipl
386(1)
8.9.2 Function MCAbipl
386(5)
8.9.3 Function CATPCAbipl
391(3)
8.9.4 Function CATPCAbipl.predregions
394(1)
8.9.5 Function PCAbipl.cat
394(1)
8.10 Revisiting the remuneration data: examples of MCA and categorical PCA biplots
394(11)
9 Generalized biplots
405(18)
9.1 Introduction
405(1)
9.2 Calculating inter-sample distances
406(2)
9.3 Constructing a generalized biplot
408(1)
9.4 Reference system
408(4)
9.5 The basic points
412(1)
9.6 Interpolation
413(2)
9.7 Prediction
415(2)
9.8 An example
417(3)
9.9 Function for constructing generalized biplots
420(3)
10 Monoplots
423(22)
10.1 Multidimensional scaling
423(4)
10.2 Monoplots related to the covariance matrix
427(9)
10.2.1 Covariance plots
427(4)
10.2.2 Correlation monoplot
431(1)
10.2.3 Coefficient of variation monoplots
431(2)
10.2.4 Other representations of correlations
433(3)
10.3 Skew-symmetry
436(4)
10.4 Area biplots
440(1)
10.5 Functions for constructing monoplots
441(4)
10.5.1 Function MonoPlot.cov
441(1)
10.5.2 Function MonoPlot.cor
442(1)
10.5.3 Function MonoPlot.cor2
443(1)
10.5.4 Function MonoPlot.coefvar
443(1)
10.5.5 Function MonoPlot.skew
443(2)
References 445(4)
Index 449
John C. Gower, Department of Mathematics, The Open University, Milton Keynes, UK. Over 100 papers. Books include Gower & Hand (1996) Biplots, in which the authors developed a unified theory of biplots.

Sugnet Gardner, British American Tobacco, Stellenbosch, South Africa.

Niel J. le Roux, Department of Statistics and Actuarial Science, University of Stellenbosch , South Africa.
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