BiplotsBiplots are the multivariate analog of scatter plots, approximating the multivariate distribution of a sample in a few dimensions to produce a graphic display. In addition, they superimpose representations of the variables on this display so that the relationships between the sample and the variable can be studied. Like scatter plots, biplots are useful for detecting patterns and for displaying the results found by more formal methods of analysis. In recent years the theory of biplots has been considerably extended. The approach adopted here is geometric, permitting a natural integration of well-known methods, such as components analysis, correspondence analysis, and canonical variate analysis as well as some newer and less well-known methods, such as nonlinear biplots and biadditive models. |
Contents
Principal components analysis PCA | 9 |
Other linear biplots | 31 |
Multiple correspondence analysis | 51 |
Canonical biplots | 86 |
Nonlinear biplots | 102 |
Generalized biplots | 121 |
Biadditive models | 142 |
Correspondence analysis CA | 175 |
Relationships between CA and MCA | 194 |
Other topics | 210 |
Algebraic results | 233 |
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Common terms and phrases
algorithm approximation axis basic points biadditive models biplot axes Burt matrix canonical categorical variables category-level centroid Chapter CLPs column-points contingency table coordinate axis coordinates correlation correspondence analysis data-matrix ddistance decomposition defined diag diagonal blocks dimensions discussed display Eckart-Young theorem eigenvectors Equation Euclidean embeddable extended matching coefficient given gives Gower graphical hence indicator matrix inner-product interpolation interpolative biplot kth variable least-squares linear biplot Mahalanobis distances markers methods minimizes Multidimensional scaling NM NM nonlinear biplots normal origin orthogonal matrix orthogonal projection planes plot prediction regions predictive biplot Procrustes Procrustes analysis pseudosamples Pythagorean distance quantitative variables reference system regression representation representing residual row and column samples scaling SF SF shown shows singular value singular value decomposition solution subspace sum-of-squares tion trajectories transformation two-dimensional unit variance vector-sum vectors x² distance zero