# PCA.Biplot: Classical PCA Biplot with added features. In MultBiplotR: Multivariate Analysis Using Biplots in R

## Description

Classical PCA Biplot with added features.

## Usage

 ```1 2``` ```PCA.Biplot(X, alpha = 1, dimension = 3, Scaling = 5, sup.rows = NULL, sup.cols = NULL, grouping = NULL) ```

## Arguments

 `X` Data Matrix `alpha` A number between 0 and 1. 0 for GH-Biplot, 1 for JK-Biplot and 0.5 for SQRT-Biplot. Use 2 or any other value not in the interval [0,1] for HJ-Biplot. `dimension` Dimension of the solution `Scaling` Transformation of the original data. See InitialTransform for available transformations. `sup.rows` Supplementary or illustrative rows, if any. `sup.cols` Supplementary or illustrative rows, if any. `grouping` A factor to standardize with the variability within groups

## Details

Biplots represent the rows and columns of a data matrix in reduced dimensions. Usually rows represent individuals, objects or samples and columns are variables measured on them. The most classical versions can be thought as visualizations associated to Principal Components Analysis (PCA) or Factor Analysis (FA) obtained from a Singular Value Decomposition or a related method. From another point of view, Classical Biplots could be obtained from regressions and calibrations that are essentially an alternated least squares algorithm equivalent to an EM-algorithm when data are normal.

## Value

An object of class ContinuousBiplot with the following components:

 `Title ` A general title `Non_Scaled_Data ` Original Data Matrix `Means ` Means of the original Variables `Medians ` Medians of the original Variables `Deviations ` Standard Deviations of the original Variables `Minima ` Minima of the original Variables `Maxima ` Maxima of the original Variables `P25 ` 25 Percentile of the original Variables `P75 ` 75 Percentile of the original Variables `Gmean ` Global mean of the complete matrix `Sup.Rows ` Supplementary rows (Non Transformed) `Sup.Cols ` Supplementary columns (Non Transformed) `Scaled_Data ` Transformed Data `Scaled_Sup.Rows` Supplementary rows (Transformed) `Scaled_Sup.Cols` Supplementary columns (Transformed) `n` Number of Rows `p` Number of Columns `nrowsSup` Number of Supplementary Rows `ncolsSup` Number of Supplementary Columns `dim` Dimension of the Biplot `EigenValues` Eigenvalues `Inertia` Explained variance (Inertia) `CumInertia` Cumulative Explained variance (Inertia) `EV` EigenVectors `Structure` Correlations of the Principal Components and the Variables `RowCoordinates` Coordinates for the rows, including the supplementary `ColCoordinates` Coordinates for the columns, including the supplementary `RowContributions` Contributions for the rows, including the supplementary `ColContributions` Contributions for the columns, including the supplementary `Scale_Factor` Scale factor for the traditional plot with points and arrows. The row coordinates are multiplied and the column coordinates divided by that scale factor. The look of the plot is better without changing the inner product. For the HJ-Biplot the scale factor is 1.

## Author(s)

Jose Luis Vicente Villardon

## References

Gabriel, K.R.(1971): The biplot graphic display of matrices with applications to principal component analysis. Biometrika, 58, 453-467.

Galindo Villardon, M. (1986). Una alternativa de representacion simultanea: HJ-Biplot. Questiio. 1986, vol. 10, núm. 1.

Gabriel, K. R. AND Zamir, S. (1979). Lower rank approximation of matrices by least squares with any choice of weights. Technometrics, 21(21):489–498, 1979.

Gabriel, K.R.(1998): Generalised Bilinear Regression. Biometrika, 85, 3, 689-700.

Gower y Hand (1996): Biplots. Chapman & Hall.

Vicente-Villardon, J. L., Galindo, M. P. and Blazquez-Zaballos, A. (2006). Logistic Biplots. Multiple Correspondence Analysis and related methods 491-509.

Demey, J., Vicente-Villardon, J. L., Galindo, M. P. and Zambrano, A. (2008). Identifying Molecular Markers Associated With Classification Of Genotypes Using External Logistic Biplots. Bioinformatics 24 2832-2838.

`InitialTransform`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```## Simple Biplot with arrows data(Protein) bip=PCA.Biplot(Protein[,3:11]) plot(bip) ## Biplot with scales on the variables plot(bip, mode="s", margin=0.2) # Structure plot (Correlations) CorrelationCircle(bip) # Plot of the Variable Contributions ColContributionPlot(bip, cex=1) ```